."},{"type":"hyper_latex","block":{"nodes":[{"text":"A square has four equal sides, so its perimeter is given by:"},{"latex":"$$$\\text{Perimeter} = 4 \\times \\htmlData{anchor=side-input}{\\color{@purple}{s}}$$"},{"text":"Substitute our side length of $7\\text{ mm}$ into the formula:"},{"latex":"$$$\\text{Perimeter} = 4 \\times \\htmlData{anchor=side-sub}{\\color{@purple}{7}} = \\htmlData{anchor=ans}{\\color{@green}{28}}\\text{ mm}$$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"side-input"},{"color":"purple","style":"text-color","anchor":"side-sub"},{"color":"green","style":"box","anchor":"ans"}],"connections":[{"to":"side-sub","from":"side-input","color":"purple","label":"substitute","style":"solid"}]},"order":2,"title":"Calculate the perimeter","description":"Multiplying the side length by $4$ gives us the perimeter of $28\\text{ mm}$. This step earns the final accuracy mark (A1)."}]},{"id":"56ab5402-b027-4d26-aedd-10665e0831c2:direct_formula","label":"Direct Formula Method","steps":[{"type":"text","order":0,"title":"Recall the direct formula","content":"To find the perimeter directly from the area of a square, we can use the direct formula:\n\n$$P = 4\\sqrt{A}$$\n\nwhere $P$ is the perimeter and $A$ is the area of the square."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A = \\htmlData{anchor=area-val}{\\color{@sky}{49}} \\text{ mm}^2$"},{"latex":"$$P = 4\\sqrt{\\htmlData{anchor=area-sub}{\\color{@sky}{A}}}$"},{"latex":"$$P = 4\\sqrt{\\htmlData{anchor=calc-sub}{\\color{@sky}{49}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"area-val"},{"color":"sky","style":"text-color","anchor":"area-sub"}],"connections":[{"to":"area-sub","from":"area-val","color":"sky","label":"substitute area","style":"solid"}]},"order":1,"title":"Substitute the given area","description":"We substitute our given area value into the formula."},{"type":"text","order":2,"title":"Calculate the final perimeter","content":"First, evaluate the square root:\n\n$$\\sqrt{49} = 7$$\n\n*(This step earns you the first mark M1)*\n\nNow, multiply by $4$ to find the perimeter:\n\n$$P = 4 \\times 7 = 28\\text{ mm}$$\n\n*(This earns you the final accuracy mark A1)*","highlights":[{"text":"49","location":"specification"}]}]}],"generatedAt":"2026-06-12T13:24:30.266Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"5343f430-1f80-4e21-b59c-3be96ae0ec2d","revisionId":"3bf4d2f3-a193-4b4c-a008-db26ad404847","questionNumber":null,"questionType":"LA","specification":"The diagram shows a paved patio area in the shape of a trapezium.\n\n![A diagram of a trapezium with parallel sides 6 m and 15 m, and height 8 m.](https://assets.mathsgenie.co.uk/questions/f49f311f-0f3a-4dcf-834e-4337ed4f847f.png)","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"da022110-78bc-4435-9cb8-29d18ccb9a33","label":"a","content":"Find the area of the patio.","markscheme":"- Applies trapezium area formula: $\\frac{1}{2}(6 + 15) \\times 8$ M1\n- Simplifies calculation: $10.5 \\times 8$ or $21 \\times 4$ M1\n- Final answer: $84$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Method shown for applying the area formula with values 6, 15, and 8.","code":"M"},{"id":"p2","marks":1,"description":"Intermediate simplification step (e.g., finding the sum 21 or dividing 8 by 2).","code":"M"},{"id":"p3","marks":1,"description":"Correct final area result.","code":"A"}],"finalAnswers":["84"],"generatedAt":"2026-05-06T13:58:45.957Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"trapezium_formula","label":"Use the trapezium formula","steps":[{"type":"text","order":0,"title":"Identify the measurements","content":"The parallel sides are $6\\text{ m}$ and $15\\text{ m}$. The perpendicular height is $8\\text{ m}$; it is the dashed vertical distance between the parallel sides.","highlights":[{"text":"Fin

Area and Perimeter

Question 28

Area and Perimeter Questions

Area and Perimeter

Question 28

Area and Perimeter Questions