33:I[196793,["/_next/static/chunks/34batdc-i3b0_.js?dpl=nogit-1791217996","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1791217996","/_next/static/chunks/0zcakt1-boe_f.js?dpl=nogit-1791217996","/_next/static/chunks/0yuh9obhrf6py.js?dpl=nogit-1791217996","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1791217996","/_next/static/chunks/2x_dbpl3b_l2r.js?dpl=nogit-1791217996","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1791217996","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1791217996","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1791217996","/_next/static/chunks/0d3f1nmeak_z5.js?dpl=nogit-1791217996","/_next/static/chunks/2gjyu-jrwu-fu.js?dpl=nogit-1791217996","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1791217996","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1791217996","/_next/static/chunks/3kzt2piec6aoa.js?dpl=nogit-1791217996","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1791217996","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1791217996","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1791217996","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1791217996","/_next/static/chunks/10rmxw_yiwj40.js?dpl=nogit-1791217996","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1791217996","/_next/static/chunks/2g-t2n9ahs3tn.js?dpl=nogit-1791217996","/_next/static/chunks/1g1suj21ijg7y.js?dpl=nogit-1791217996","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1791217996","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1791217996","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1791217996","/_next/static/chunks/2oijhb0tdir9b.js?dpl=nogit-1791217996","/_next/static/chunks/2eanemqjnv2vr.js?dpl=nogit-1791217996","/_next/static/chunks/44nm8-o05iplc.js?dpl=nogit-1791217996","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1791217996","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1791217996","/_next/static/chunks/2r29ujce72_54.js?dpl=nogit-1791217996","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1791217996","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1791217996","/_next/static/chunks/0jt4ynafgg-jc.js?dpl=nogit-1791217996","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1791217996","/_next/static/chunks/0qdwqau744_ry.js?dpl=nogit-1791217996","/_next/static/chunks/2eycy5cqzjdqf.js?dpl=nogit-1791217996","/_next/static/chunks/33z1jiacs_jrz.js?dpl=nogit-1791217996","/_next/static/chunks/0w7ow4sfu0tl_.js?dpl=nogit-1791217996","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1791217996","/_next/static/chunks/1eyu-5752jh17.js?dpl=nogit-1791217996","/_next/static/chunks/28uw5fp_u1bnm.js?dpl=nogit-1791217996","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1791217996","/_next/static/chunks/0ixdj_i1afhld.js?dpl=nogit-1791217996","/_next/static/chunks/20_c60cgo1g9g.js?dpl=nogit-1791217996","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1791217996","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1791217996","/_next/static/chunks/2ryoj58czm802.js?dpl=nogit-1791217996","/_next/static/chunks/3v6lxgtmi9vqz.js?dpl=nogit-1791217996","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1791217996","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1791217996","/_next/static/chunks/0wl6wuakgnlec.js?dpl=nogit-1791217996","/_next/static/chunks/30w6c7jj-mxyi.js?dpl=nogit-1791217996","/_next/static/chunks/2qk8b2y5gyu_0.js?dpl=nogit-1791217996","/_next/static/chunks/3lwy4_ovl68-o.js?dpl=nogit-1791217996","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1791217996","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1791217996","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1791217996","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1791217996","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1791217996","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1791217996"],"Gingerbread"] 35:I[647935,["/_next/static/chunks/34batdc-i3b0_.js?dpl=nogit-1791217996","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1791217996","/_next/static/chunks/0zcakt1-boe_f.js?dpl=nogit-1791217996","/_next/static/chunks/0yuh9obhrf6py.js?dpl=nogit-1791217996","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1791217996","/_next/static/chunks/2x_dbpl3b_l2r.js?dpl=nogit-1791217996","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1791217996","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1791217996","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1791217996","/_next/static/chunks/0d3f1nmeak_z5.js?dpl=nogit-1791217996","/_next/static/chunks/2gjyu-jrwu-fu.js?dpl=nogit-1791217996","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1791217996","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1791217996","/_next/static/chunks/3kzt2piec6aoa.js?dpl=nogit-1791217996","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1791217996","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1791217996","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1791217996","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1791217996","/_next/static/chunks/10rmxw_yiwj40.js?dpl=nogit-1791217996","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1791217996","/_next/static/chunks/2g-t2n9ahs3tn.js?dpl=nogit-1791217996","/_next/static/chunks/1g1suj21ijg7y.js?dpl=nogit-1791217996","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1791217996","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1791217996","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1791217996","/_next/static/chunks/2oijhb0tdir9b.js?dpl=nogit-1791217996","/_next/static/chunks/2eanemqjnv2vr.js?dpl=nogit-1791217996","/_next/static/chunks/44nm8-o05iplc.js?dpl=nogit-1791217996","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1791217996","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1791217996","/_next/static/chunks/2r29ujce72_54.js?dpl=nogit-1791217996","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1791217996","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1791217996","/_next/static/chunks/0jt4ynafgg-jc.js?dpl=nogit-1791217996","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1791217996","/_next/static/chunks/0qdwqau744_ry.js?dpl=nogit-1791217996","/_next/static/chunks/2eycy5cqzjdqf.js?dpl=nogit-1791217996","/_next/static/chunks/33z1jiacs_jrz.js?dpl=nogit-1791217996","/_next/static/chunks/0w7ow4sfu0tl_.js?dpl=nogit-1791217996","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1791217996","/_next/static/chunks/1eyu-5752jh17.js?dpl=nogit-1791217996","/_next/static/chunks/28uw5fp_u1bnm.js?dpl=nogit-1791217996","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1791217996","/_next/static/chunks/0ixdj_i1afhld.js?dpl=nogit-1791217996","/_next/static/chunks/20_c60cgo1g9g.js?dpl=nogit-1791217996","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1791217996","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1791217996","/_next/static/chunks/2ryoj58czm802.js?dpl=nogit-1791217996","/_next/static/chunks/3v6lxgtmi9vqz.js?dpl=nogit-1791217996","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1791217996","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1791217996","/_next/static/chunks/0wl6wuakgnlec.js?dpl=nogit-1791217996","/_next/static/chunks/30w6c7jj-mxyi.js?dpl=nogit-1791217996","/_next/static/chunks/2qk8b2y5gyu_0.js?dpl=nogit-1791217996","/_next/static/chunks/3lwy4_ovl68-o.js?dpl=nogit-1791217996","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1791217996","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1791217996","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1791217996","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1791217996","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1791217996","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1791217996"],"RecordResourceResume"] 36:I[830476,["/_next/static/chunks/34batdc-i3b0_.js?dpl=nogit-1791217996","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1791217996","/_next/static/chunks/0zcakt1-boe_f.js?dpl=nogit-1791217996","/_next/static/chunks/0yuh9obhrf6py.js?dpl=nogit-1791217996","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1791217996","/_next/static/chunks/2x_dbpl3b_l2r.js?dpl=nogit-1791217996","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1791217996","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1791217996","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1791217996","/_next/static/chunks/0d3f1nmeak_z5.js?dpl=nogit-1791217996","/_next/static/chunks/2gjyu-jrwu-fu.js?dpl=nogit-1791217996","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1791217996","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1791217996","/_next/static/chunks/3kzt2piec6aoa.js?dpl=nogit-1791217996","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1791217996","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1791217996","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1791217996","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1791217996","/_next/static/chunks/10rmxw_yiwj40.js?dpl=nogit-1791217996","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1791217996","/_next/static/chunks/2g-t2n9ahs3tn.js?dpl=nogit-1791217996","/_next/static/chunks/1g1suj21ijg7y.js?dpl=nogit-1791217996","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1791217996","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1791217996","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1791217996","/_next/static/chunks/2oijhb0tdir9b.js?dpl=nogit-1791217996","/_next/static/chunks/2eanemqjnv2vr.js?dpl=nogit-1791217996","/_next/static/chunks/44nm8-o05iplc.js?dpl=nogit-1791217996","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1791217996","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1791217996","/_next/static/chunks/2r29ujce72_54.js?dpl=nogit-1791217996","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1791217996","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1791217996","/_next/static/chunks/0jt4ynafgg-jc.js?dpl=nogit-1791217996","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1791217996","/_next/static/chunks/0qdwqau744_ry.js?dpl=nogit-1791217996","/_next/static/chunks/2eycy5cqzjdqf.js?dpl=nogit-1791217996","/_next/static/chunks/33z1jiacs_jrz.js?dpl=nogit-1791217996","/_next/static/chunks/0w7ow4sfu0tl_.js?dpl=nogit-1791217996","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1791217996","/_next/static/chunks/1eyu-5752jh17.js?dpl=nogit-1791217996","/_next/static/chunks/28uw5fp_u1bnm.js?dpl=nogit-1791217996","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1791217996","/_next/static/chunks/0ixdj_i1afhld.js?dpl=nogit-1791217996","/_next/static/chunks/20_c60cgo1g9g.js?dpl=nogit-1791217996","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1791217996","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1791217996","/_next/static/chunks/2ryoj58czm802.js?dpl=nogit-1791217996","/_next/static/chunks/3v6lxgtmi9vqz.js?dpl=nogit-1791217996","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1791217996","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1791217996","/_next/static/chunks/0wl6wuakgnlec.js?dpl=nogit-1791217996","/_next/static/chunks/30w6c7jj-mxyi.js?dpl=nogit-1791217996","/_next/static/chunks/2qk8b2y5gyu_0.js?dpl=nogit-1791217996","/_next/static/chunks/3lwy4_ovl68-o.js?dpl=nogit-1791217996","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1791217996","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1791217996","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1791217996","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1791217996","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1791217996","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1791217996"],"FlashcardAccessBranch"] 37:I[315438,["/_next/static/chunks/34batdc-i3b0_.js?dpl=nogit-1791217996","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1791217996","/_next/static/chunks/0zcakt1-boe_f.js?dpl=nogit-1791217996","/_next/static/chunks/0yuh9obhrf6py.js?dpl=nogit-1791217996","/_next/static/chunks/3mz725-y91ph6.js?dpl=nogit-1791217996","/_next/static/chunks/2x_dbpl3b_l2r.js?dpl=nogit-1791217996","/_next/static/chunks/13_9hjun60hj-.js?dpl=nogit-1791217996","/_next/static/chunks/2bxmml65nu49g.js?dpl=nogit-1791217996","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1791217996","/_next/static/chunks/0d3f1nmeak_z5.js?dpl=nogit-1791217996","/_next/static/chunks/2gjyu-jrwu-fu.js?dpl=nogit-1791217996","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1791217996","/_next/static/chunks/3jpl-42mbad5n.js?dpl=nogit-1791217996","/_next/static/chunks/3kzt2piec6aoa.js?dpl=nogit-1791217996","/_next/static/chunks/19ijf68pshdcn.js?dpl=nogit-1791217996","/_next/static/chunks/2os7nxouq91eq.js?dpl=nogit-1791217996","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1791217996","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1791217996","/_next/static/chunks/10rmxw_yiwj40.js?dpl=nogit-1791217996","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1791217996","/_next/static/chunks/2g-t2n9ahs3tn.js?dpl=nogit-1791217996","/_next/static/chunks/1g1suj21ijg7y.js?dpl=nogit-1791217996","/_next/static/chunks/3lz9pr5v38m4h.js?dpl=nogit-1791217996","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1791217996","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1791217996","/_next/static/chunks/2oijhb0tdir9b.js?dpl=nogit-1791217996","/_next/static/chunks/2eanemqjnv2vr.js?dpl=nogit-1791217996","/_next/static/chunks/44nm8-o05iplc.js?dpl=nogit-1791217996","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1791217996","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1791217996","/_next/static/chunks/2r29ujce72_54.js?dpl=nogit-1791217996","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1791217996","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1791217996","/_next/static/chunks/0jt4ynafgg-jc.js?dpl=nogit-1791217996","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1791217996","/_next/static/chunks/0qdwqau744_ry.js?dpl=nogit-1791217996","/_next/static/chunks/2eycy5cqzjdqf.js?dpl=nogit-1791217996","/_next/static/chunks/33z1jiacs_jrz.js?dpl=nogit-1791217996","/_next/static/chunks/0w7ow4sfu0tl_.js?dpl=nogit-1791217996","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1791217996","/_next/static/chunks/1eyu-5752jh17.js?dpl=nogit-1791217996","/_next/static/chunks/28uw5fp_u1bnm.js?dpl=nogit-1791217996","/_next/static/chunks/3ybwgs28on6c8.js?dpl=nogit-1791217996","/_next/static/chunks/0ixdj_i1afhld.js?dpl=nogit-1791217996","/_next/static/chunks/20_c60cgo1g9g.js?dpl=nogit-1791217996","/_next/static/chunks/075i0tnxt4not.js?dpl=nogit-1791217996","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1791217996","/_next/static/chunks/2ryoj58czm802.js?dpl=nogit-1791217996","/_next/static/chunks/3v6lxgtmi9vqz.js?dpl=nogit-1791217996","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1791217996","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1791217996","/_next/static/chunks/0wl6wuakgnlec.js?dpl=nogit-1791217996","/_next/static/chunks/30w6c7jj-mxyi.js?dpl=nogit-1791217996","/_next/static/chunks/2qk8b2y5gyu_0.js?dpl=nogit-1791217996","/_next/static/chunks/3lwy4_ovl68-o.js?dpl=nogit-1791217996","/_next/static/chunks/1hnuhh5t7cfaj.js?dpl=nogit-1791217996","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1791217996","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1791217996","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1791217996","/_next/static/chunks/1d7tjnrc0fv5y.js?dpl=nogit-1791217996","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1791217996"],"TopicFlashcardRunner"] 24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/edexcel/grade-4-4-12-surface-area/flashcards","label":"Surface Area","subjectCode":"gcse_maths","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"db6675f9-3255-465d-a2ec-69c2397cdb9e","title":"Surface Area Flashcards","topicId":"71ef37aa-b034-47c9-be14-02918f0c4239","topicSlug":"grade-4-4-12-surface-area","cards":[{"id":"56fef617-1763-49d5-b3ac-a86eea009317","cardType":"cloze","points":null,"front":"Surface area is the total area of all the [ ] of a 3D shape.","back":"Surface area is the total area of all the outside faces of a 3D shape.","mcqOptions":[{"text":"outside faces","correct":true,"explanation":"Surface area is found by adding the areas of every outside face of a 3D shape. Only the surfaces exposed on the exterior are included."},{"text":"inside angles","correct":false,"explanation":"Angles describe turns between edges and do not have an area. The correct term is outside faces, because surface area totals the exterior surfaces of the shape."},{"text":"vertical edges","correct":false,"explanation":"Edges are one-dimensional lengths, so adding them would not give an area. Surface area is the total area of all the outside faces."},{"text":"corner points","correct":false,"explanation":"Corner points, or vertices, have no area and are counted rather than measured. The required term is outside faces, whose areas combine to give surface area."}]},{"id":"de3eafa4-ff5f-4b69-8897-1d7ef457b448","cardType":"basic","points":1,"front":"Surface area is measured in what type of units?","back":"Square units, e.g. cm² or m².","mcqOptions":[{"text":"Square units, e.g. cm² or m².","correct":true,"explanation":"Area measures two-dimensional space, so each length unit is multiplied by another length unit. This produces square units such as cm² or m²."},{"text":"Linear units, e.g. cm or m.","correct":false,"explanation":"Linear units measure one-dimensional quantities such as length or perimeter. Surface area is two-dimensional, so it is measured in square units such as cm² or m²."},{"text":"Cubic units, e.g. cm³ or m³.","correct":false,"explanation":"Cubic units measure three-dimensional volume, not the area covering a shape. Surface area is measured in square units such as cm² or m²."},{"text":"Angle units, e.g. degrees or radians.","correct":false,"explanation":"Degrees and radians measure angles rather than the size of surfaces. Surface area measures two-dimensional regions, so square units such as cm² or m² are required."}]},{"id":"248eae5f-f691-47ad-b4c5-0ad257341115","cardType":"basic","points":1,"front":"What formula is used for the area of a rectangular face?","back":"$\\text{length}\\times\\text{width}$","mcqOptions":[{"text":"$\\text{length}\\times\\text{width}$","correct":true,"explanation":"A rectangle’s area is found by multiplying its two perpendicular dimensions. Therefore, the area of a rectangular face is length multiplied by width."},{"text":"$2\\times\\text{length}+2\\times\\text{width}$","correct":false,"explanation":"This adds the four side lengths and therefore calculates the rectangle’s perimeter. Its area is found using length multiplied by width."},{"text":"$\\frac{1}{2}\\times\\text{length}\\times\\text{width}$","correct":false,"explanation":"The factor of one-half belongs to the triangle area formula. A rectangular face occupies twice that triangular area, so its formula is length multiplied by width."},{"text":"$\\text{length}+\\text{width}$","correct":false,"explanation":"Adding the dimensions does not calculate either the complete perimeter or the enclosed area. The area of a rectangular face is length multiplied by width."}]},{"id":"5cb399ef-5f69-4ef1-af54-c38985de54ed","cardType":"cloze","points":null,"front":"The perpendicular height is measured [ ], not along a slanted side.","back":"The perpendicular height is measured at 90° to the base, not along a slanted side.","mcqOptions":[{"text":"at 90° to the base","correct":true,"explanation":"Perpendicular lines meet at a right angle, so the perpendicular height must be measured at 90° to the base rather than along a sloping side."},{"text":"parallel to the base","correct":false,"explanation":"A line parallel to the base never forms the required height between the base and opposite point. The perpendicular height is measured at 90° to the base."},{"text":"along the longest side","correct":false,"explanation":"The longest side may be slanted and therefore may not represent the shortest distance from the base. The perpendicular height is measured at 90° to the base."},{"text":"at 45° to the base","correct":false,"explanation":"A 45° line is diagonal rather than perpendicular, so using it gives an incorrect height. The perpendicular height must be measured at 90° to the base."}]},{"id":"48ba13b0-74a7-451c-b740-e365ecfd2952","cardType":"cloze","points":null,"front":"Triangle area: [ ], where $h$ is the perpendicular height.","back":"Triangle area: $A=\\frac{1}{2}bh$, where $h$ is the perpendicular height.","mcqOptions":[{"text":"$$A=\\frac{1}{2}bh$","correct":true,"explanation":"A triangle occupies half the area of a rectangle with the same base and perpendicular height. Its area is therefore one-half multiplied by base multiplied by height."},{"text":"$$A=bh$","correct":false,"explanation":"This calculates the area of a rectangle or parallelogram with base $b$ and height $h$. A triangle has half that area, so $A=\\frac{1}{2}bh$."},{"text":"$$A=\\frac{1}{2}(b+h)$","correct":false,"explanation":"Adding base and height combines lengths and cannot produce square units. Triangle area requires multiplying them and halving the result: $A=\\frac{1}{2}bh$."},{"text":"$$A=2bh$","correct":false,"explanation":"This doubles the corresponding rectangle’s area instead of taking half of it. A triangle with base $b$ and perpendicular height $h$ has area $A=\\frac{1}{2}bh$."}]},{"id":"f421d731-d96a-4f63-8a99-572a4d0f50af","cardType":"cloze","points":null,"front":"Trapezium area: [ ], where $a$ and $b$ are parallel sides.","back":"Trapezium area: $A=\\frac{1}{2}(a+b)h$, where $a$ and $b$ are parallel sides.","mcqOptions":[{"text":"$$A=\\frac{1}{2}(a+b)h$","correct":true,"explanation":"The area of a trapezium equals its average parallel-side length, $\\frac{a+b}{2}$, multiplied by its perpendicular height. This gives $A=\\frac{1}{2}(a+b)h$."},{"text":"$$A=(a+b)h$","correct":false,"explanation":"This uses the sum rather than the average of the parallel sides, making the area twice as large. The correct formula is $A=\\frac{1}{2}(a+b)h$."},{"text":"$$A=\\frac{1}{2}abh$","correct":false,"explanation":"Multiplying both parallel sides together introduces an extra length factor and gives cubic units. Their lengths must be added, so $A=\\frac{1}{2}(a+b)h$."},{"text":"$$A=\\frac{1}{2}(a-b)h$","correct":false,"explanation":"Subtracting the parallel sides finds their difference, not their average length. They must be added before multiplying by half the height: $A=\\frac{1}{2}(a+b)h$."}]},{"id":"9afc1b8f-7702-40d6-bf64-9a12d9114274","cardType":"basic","points":2,"front":"A trapezium has parallel sides 12 cm and 6 cm, height 5 cm. What is its area?","back":"45 cm²","mcqOptions":[{"text":"45 cm²","correct":true,"explanation":"Using $A=\\frac{1}{2}(a+b)h$ gives $\\frac{1}{2}(12+6)\\times5=\\frac{1}{2}\\times18\\times5=45$ cm²."},{"text":"90 cm²","correct":false,"explanation":"This omits the factor of one-half and calculates $(12+6)\\times5$. Averaging the parallel sides gives $\\frac{1}{2}(12+6)\\times5=45$ cm²."},{"text":"30 cm²","correct":false,"explanation":"This uses only the 12 cm side and halves $12\\times5$, ignoring the other parallel side. The trapezium formula gives $45$ cm²."},{"text":"15 cm²","correct":false,"explanation":"This incorrectly uses half the difference between the parallel sides: $\\frac{1}{2}(12-6)\\times5$. Their lengths must be added, giving $45$ cm²."}]},{"id":"a98469ba-7588-47f7-8a18-b11ebabddf9a","cardType":"basic","points":2,"front":"Why do you double the three different face areas for a cuboid?","back":"Opposite faces are the same size.","mcqOptions":[{"text":"Opposite faces are the same size.","correct":true,"explanation":"A cuboid has three pairs of opposite faces. The two faces in each pair have identical dimensions and areas, so each different face area is counted twice."},{"text":"Adjacent faces are the same shape.","correct":false,"explanation":"Adjacent faces can have different dimensions and areas, even though each is rectangular. Doubling works because opposite faces are the same size and form three matching pairs."},{"text":"Opposite edges are the same length.","correct":false,"explanation":"Equal opposite edge lengths help define the cuboid, but they do not directly explain doubling face areas. Each area is doubled because opposite faces are the same size."},{"text":"All six faces have the same area.","correct":false,"explanation":"All six faces have equal area only for a cube, not for every cuboid. A general cuboid has three pairs in which opposite faces are the same size."}]},{"id":"710aa801-bddd-4ebb-9589-425c6a48509e","cardType":"cloze","points":null,"front":"Cuboid total surface area: [ ].","back":"Cuboid total surface area: $2lw+2lh+2wh$.","mcqOptions":[{"text":"$$2lw+2lh+2wh$","correct":true,"explanation":"A cuboid has two faces of each area $lw$, $lh$ and $wh$, so its total surface area is $2lw+2lh+2wh$."},{"text":"$$lw+lh+wh$","correct":false,"explanation":"This counts only one face of each size. A cuboid has two of every face, so the correct formula is $2lw+2lh+2wh$."},{"text":"$$2lw+lh+wh$","correct":false,"explanation":"This doubles only the $lw$ face, leaving the other two pairs undercounted. All three face areas must be doubled, giving $2lw+2lh+2wh$."},{"text":"$$2l+2w+2h$","correct":false,"explanation":"This adds edge lengths rather than face areas, so it cannot calculate surface area. Multiplying pairs of dimensions gives the correct formula $2lw+2lh+2wh$."}]},{"id":"a3e24811-8a15-44f2-8ff6-d0c085a57396","cardType":"basic","points":2,"front":"A cuboid is 9 cm by 4 cm by 3 cm. What is its total surface area?","back":"150 cm²","mcqOptions":[{"text":"150 cm²","correct":true,"explanation":"The three different face areas are $9\\times4=36$, $9\\times3=27$ and $4\\times3=12$. Doubling their sum gives $2(36+27+12)=150$ cm²."},{"text":"75 cm²","correct":false,"explanation":"This adds one face of each size but forgets that every face has an opposite matching face. Doubling $36+27+12$ gives the correct total of 150 cm²."},{"text":"108 cm²","correct":false,"explanation":"This is the volume, found by multiplying all three dimensions, rather than the total area of the faces. The surface area is $2(36+27+12)=150$ cm²."},{"text":"138 cm²","correct":false,"explanation":"This counts only one $4\\times3$ face instead of two. Including both of every face gives $72+54+24=150$ cm²."}]},{"id":"da59f0d9-477d-4594-8dfd-a97a2fab36d7","cardType":"cloze","points":null,"front":"A prism has the same shape all the way through; the repeated end shape is the [ ].","back":"A prism has the same shape all the way through; the repeated end shape is the cross-section.","mcqOptions":[{"text":"cross-section","correct":true,"explanation":"The cross-section is the repeated two-dimensional end shape that remains identical along the entire length of a prism."},{"text":"side elevation","correct":false,"explanation":"A side elevation is a two-dimensional view of an object, not necessarily its repeated end shape. The repeated shape running through a prism is its cross-section."},{"text":"surface area","correct":false,"explanation":"Surface area is the total area of all the prism’s outer faces, not the repeated end shape. That repeated shape is called the cross-section."},{"text":"longitudinal section","correct":false,"explanation":"A longitudinal section is a cut made along an object’s length. The identical end shape repeated through a prism is instead called its cross-section."}]},{"id":"ad3e0416-1136-4114-917d-cbf7e27b5a81","cardType":"basic","points":1,"front":"What formula gives the total surface area of any prism?","back":"$2\\times\\text{cross-section area}+\\text{perimeter}\\times\\text{length}$","mcqOptions":[{"text":"$2\\times\\text{cross-section area}+\\text{perimeter}\\times\\text{length}$","correct":true,"explanation":"The two congruent ends contribute twice the cross-section area, while unfolding the side faces produces rectangles with combined area equal to perimeter times length."},{"text":"$\\text{cross-section area}+\\text{perimeter}\\times\\text{length}$","correct":false,"explanation":"This includes only one of the two congruent end faces. Both ends must be counted, so the formula begins with $2\\times\\text{cross-section area}$."},{"text":"$2\\times\\text{cross-section area}+\\text{perimeter}+\\text{length}$","correct":false,"explanation":"Adding perimeter and length does not produce an area because both are one-dimensional measurements. Their product gives the area of the rectangular side faces."},{"text":"$2\\times\\text{cross-section area}+2\\times\\text{perimeter}\\times\\text{length}$","correct":false,"explanation":"This doubles the side-face area unnecessarily. The perimeter already includes every edge around the cross-section, so the correct side-face term is just perimeter times length."}]},{"id":"73b3a90b-91a6-4475-8a5d-49597347ce1e","cardType":"basic","points":1,"front":"In the prism formula, what does $\\text{perimeter}\\times\\text{length}$ find?","back":"The rectangular side faces.","mcqOptions":[{"text":"The rectangular side faces.","correct":true,"explanation":"Each cross-section edge forms a rectangle whose other dimension is the prism’s length. Adding these rectangles gives the cross-section perimeter multiplied by the length."},{"text":"The two cross-section faces.","correct":false,"explanation":"The two end faces are found using twice the cross-section area. Perimeter multiplied by length instead gives the combined area of the rectangular side faces."},{"text":"The volume inside the prism.","correct":false,"explanation":"Volume is found by multiplying cross-section area by length. Multiplying the cross-section perimeter by length finds the combined area of the rectangular side faces."},{"text":"The perimeter of each end.","correct":false,"explanation":"The perimeter is already one factor in the calculation. Multiplying it by the prism’s length converts the boundary strips into the total area of the rectangular side faces."}]},{"id":"149ad0ed-55f1-492e-bf6e-57e059c177a5","cardType":"basic","points":2,"front":"Triangular prism: cross-section perimeter 36 cm, length 7 cm. What is the side-face area?","back":"252 cm²","mcqOptions":[{"text":"252 cm²","correct":true,"explanation":"The side-face area of a prism is cross-section perimeter multiplied by length. Therefore, $36\\times7=252$, giving a side-face area of 252 cm²."},{"text":"43 cm²","correct":false,"explanation":"This comes from adding 36 and 7 instead of multiplying them. Side-face area is perimeter times length, so $36\\times7=252$ cm²."},{"text":"126 cm²","correct":false,"explanation":"This incorrectly halves the product, perhaps treating the side faces like a triangle. They are rectangles, so the full calculation is $36\\times7=252$ cm²."},{"text":"504 cm²","correct":false,"explanation":"This doubles the product unnecessarily. The perimeter already includes every side of the triangular cross-section, so $36\\times7=252$ cm² is the complete side-face area."}]},{"id":"bed5ee0b-a959-46fa-b114-bc4aeaf0f5c9","cardType":"basic","points":2,"front":"How do you find the area of an L-shaped end made by removing a corner from a rectangle?","back":"Subtract the missing rectangle’s area.","mcqOptions":[{"text":"Subtract the missing rectangle’s area.","correct":true,"explanation":"The L-shape is the complete outer rectangle with a smaller rectangular corner removed, so subtracting the missing rectangle’s area leaves the required L-shaped area."},{"text":"Add the missing rectangle’s area.","correct":false,"explanation":"Adding would include the removed corner and make the result larger than the outer rectangle. The missing rectangle’s area must be subtracted from the outer rectangle’s area."},{"text":"Subtract the missing rectangle’s perimeter.","correct":false,"explanation":"Perimeter measures boundary length and cannot be subtracted from an area. Find both rectangular areas, then subtract the missing rectangle’s area from the outer rectangle’s area."},{"text":"Multiply the missing rectangle’s area.","correct":false,"explanation":"Multiplying areas does not represent removing a corner and produces the wrong units. Subtract the missing rectangle’s area from the area of the complete outer rectangle."}]},{"id":"8412f892-43cc-416d-9631-39a32066e4e5","cardType":"basic","points":2,"front":"An L-shaped end fits inside 8 cm by 7 cm, with a 3 cm by 4 cm corner removed. What is its area?","back":"44 cm²","mcqOptions":[{"text":"44 cm²","correct":true,"explanation":"The complete outer rectangle has area $8\\times7=56$ cm², and the removed corner has area $3\\times4=12$ cm². Therefore, $56-12=44$ cm²."},{"text":"68 cm²","correct":false,"explanation":"This adds the missing corner’s area to the outer rectangle instead of removing it. The correct calculation is $56-12=44$ cm²."},{"text":"12 cm²","correct":false,"explanation":"This is only the area of the removed $3$ cm by $4$ cm corner. Subtracting it from the outer area gives $56-12=44$ cm²."},{"text":"56 cm²","correct":false,"explanation":"This is the area of the complete $8$ cm by $7$ cm rectangle and ignores the removed corner. Subtracting $12$ cm² gives 44 cm²."}]},{"id":"47712028-177e-4810-8994-9ce79bbd5e7e","cardType":"basic","points":2,"front":"Why trace around a composite cross-section when finding perimeter?","back":"To include the step edges.","mcqOptions":[{"text":"To include the step edges.","correct":true,"explanation":"Tracing the outside boundary ensures that every exposed edge is counted, including the short step edges that are easy to overlook in a composite cross-section."},{"text":"To include the internal joins.","correct":false,"explanation":"Internal joins are not exposed parts of the perimeter and must not be counted. Tracing is used to include all outside edges, especially the step edges."},{"text":"To include the face areas.","correct":false,"explanation":"Face areas are needed for surface area, not perimeter. Tracing the boundary helps identify all exposed lengths, including the step edges."},{"text":"To include the diagonal lengths.","correct":false,"explanation":"Diagonal lengths are not automatically part of a composite cross-section’s boundary. The purpose of tracing is to ensure the step edges are included."}]},{"id":"2b1e1a37-f49e-41b3-92bf-e4550a2b74b7","cardType":"basic","points":1,"front":"How many circular faces does a closed cylinder have?","back":"Two equal circular faces.","mcqOptions":[{"text":"Two equal circular faces.","correct":true,"explanation":"A closed cylinder has a circular face at each end. These two circles have the same radius, so they are equal in area."},{"text":"One circular face.","correct":false,"explanation":"One circular face describes an open cylinder with one end missing. A closed cylinder has two equal circular faces, one at each end."},{"text":"Three equal circular faces.","correct":false,"explanation":"The curved surface is not a circular face. A closed cylinder has exactly two equal circular faces, located at its two ends."},{"text":"Two unequal circular faces.","correct":false,"explanation":"A cylinder’s two end circles must be equal because they share the same radius. A closed cylinder therefore has two equal circular faces."}]},{"id":"4e76d3f8-3fd0-4e40-87d5-f1a3f3de230e","cardType":"cloze","points":null,"front":"Closed cylinder total surface area: [ ].","back":"Closed cylinder total surface area: $2\\pi r^2+2\\pi rh$.","mcqOptions":[{"text":"$$2\\pi r^2+2\\pi rh$","correct":true,"explanation":"The two circular ends have combined area $2\\pi r^2$, while the curved surface has area $2\\pi rh$. Adding them gives the total surface area."},{"text":"$$\\pi r^2+2\\pi rh$","correct":false,"explanation":"This includes only one circular end, omitting the second area of $\\pi r^2$. A closed cylinder requires $2\\pi r^2+2\\pi rh$."},{"text":"$$2\\pi r^2$","correct":false,"explanation":"This adds the two circular ends but omits the curved surface. The curved area is $2\\pi rh$, so the full formula is $2\\pi r^2+2\\pi rh$."},{"text":"$$2\\pi r^2+\\pi rh$","correct":false,"explanation":"The curved surface uses the circumference $2\\pi r$ multiplied by height, not $\\pi r$ multiplied by height. The correct total is $2\\pi r^2+2\\pi rh$."}]},{"id":"31d951a0-3fce-4d4e-8c34-a727c0f60d21","cardType":"basic","points":1,"front":"If a cylinder question gives the diameter, what must you do first?","back":"Halve it to get the radius.","mcqOptions":[{"text":"Halve it to get the radius.","correct":true,"explanation":"The radius is the distance from the centre to the circumference, which is half the diameter. Therefore, divide the given diameter by two first."},{"text":"Double it to get the radius.","correct":false,"explanation":"Doubling confuses the relationship between radius and diameter. The diameter is already twice the radius, so it must be halved to obtain the radius."},{"text":"Square it to get the radius.","correct":false,"explanation":"Squaring the diameter does not convert it into a radius; squaring is used later in circle-area calculations. First halve the diameter to get the radius."},{"text":"Use it as the radius.","correct":false,"explanation":"Using the diameter unchanged as the radius doubles the required length and makes area calculations four times too large. The diameter must be halved."}]},{"id":"b293d629-dcd4-423b-b308-a14efcdf5a18","cardType":"basic","points":1,"front":"If area is in cm², how do you convert it to m²?","back":"Divide by 10000.","mcqOptions":[{"text":"Divide by 10000.","correct":true,"explanation":"Since $1\\text{ m}=100\\text{ cm}$, squaring the conversion gives $1\\text{ m}^2=10000\\text{ cm}^2$. Therefore, divide a value in cm² by 10000."},{"text":"Divide by 100.","correct":false,"explanation":"Dividing by 100 applies the linear length conversion without squaring it. Area conversion requires dividing by $100^2=10000$ to change cm² into m²."},{"text":"Multiply by 10000.","correct":false,"explanation":"Multiplying by 10000 converts from m² to cm², the opposite direction. To convert the smaller cm² units into m², divide by 10000."},{"text":"Divide by 1000000.","correct":false,"explanation":"Dividing by 1000000 incorrectly uses the cubic conversion associated with cm³ and m³. For square units, divide by $100^2=10000$."}]},{"id":"f3ffa98d-87af-420d-90bf-6e4dd6deedfd","cardType":"basic","points":1,"front":"In a paint question, what do you do after dividing by coverage per pot?","back":"Round up to the next whole pot.","mcqOptions":[{"text":"Round up to the next whole pot.","correct":true,"explanation":"Any positive fraction of an additional pot means another complete pot must be bought. Rounding up ensures there is enough paint for the entire area."},{"text":"Round down to the previous whole pot.","correct":false,"explanation":"Rounding down would leave too little paint whenever the result is not already a whole number. The number of pots must always be rounded up."},{"text":"Round normally to the nearest whole pot.","correct":false,"explanation":"Rounding to the nearest whole number can round down and leave insufficient paint. Since only complete pots can be bought, always round up."},{"text":"Leave it as a decimal number of pots.","correct":false,"explanation":"A decimal result represents the calculated proportion of a pot, but shops sell whole pots. It must be rounded up to the next whole pot."}]},{"id":"e1ed32fa-db39-431b-a15e-919fd30317e9","cardType":"basic","points":2,"front":"Four boxes need 10.24 m² of paint. One pot covers 3 m². How many pots are needed?","back":"4 pots","mcqOptions":[{"text":"4 pots","correct":true,"explanation":"Dividing the required area by the coverage gives $10.24\\div3\\approx3.41$. Since only whole pots can be bought, this must be rounded up to 4 pots."},{"text":"3 pots","correct":false,"explanation":"Three pots cover only $3\\times3=9$ m², which is less than 10.24 m². The calculation gives about 3.41, so 4 pots are required."},{"text":"3.41 pots","correct":false,"explanation":"This is the unrounded result of $10.24\\div3$, but paint is purchased in complete pots. About 3.41 pots must be rounded up to 4 pots."},{"text":"5 pots","correct":false,"explanation":"Rounding $10.24\\div3\\approx3.41$ up gives 4, not 5. Buying five pots would provide more complete pots than the calculation requires."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Surface Area","title":"Surface Area Flashcards","topbar":{"backHref":"/gcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"71ef37aa-b034-47c9-be14-02918f0c4239","walled":"$L39"}],"$L3a","$L3b"]