cheme":"- Applies area of a triangle formula: $\\frac{\\text{base} \\times \\text{height}}{2} = \\frac{4 \\times 9}{2}$ M1\n- Final answer: $18$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Calculation and final area of triangle R.","code":"M"}],"finalAnswers":["18"],"generatedAt":"2026-05-06T13:59:22.382Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"triangle_area","label":"Use the triangle area formula","steps":[{"type":"text","order":0,"title":"Read the dimensions","content":"Shape **R** is a triangle. Count the centimetre-grid intervals to identify a base of $4\\text{ cm}$ and its **perpendicular height** of $9\\text{ cm}$. The perpendicular height meets the base at a right angle.","highlights":[{"text":"Find the area of shape **R**.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A=\\dfrac{\\htmlData{anchor=formula_values}{\\color{@sky}{\\text{base}\\times\\text{height}}}}{2}$"},{"latex":"$$A=\\dfrac{\\htmlData{anchor=substituted_values}{\\color{@sky}{4\\times 9}}}{2}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"formula_values"},{"color":"sky","style":"text-color","anchor":"substituted_values"}],"connections":[{"to":"substituted_values","from":"formula_values","color":"sky","style":"solid"}]},"order":1,"title":"Substitute the values","description":"Use the triangle area formula. Substituting the correct base and perpendicular height earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$A=\\dfrac{4\\times 9}{2}$"},{"latex":"$$A=\\dfrac{36}{2}$"},{"latex":"$$\\htmlData{anchor=final_area}{A=18\\text{ cm}^2}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"final_area"}]},"order":2,"title":"Calculate the area","description":"Multiply the base by the height, then divide by 2. Include square centimetres because area is measured in square units. This correct final answer earns A1."}]}],"generatedAt":"2026-07-19T15:25:14.490Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"7f725ac2-be9b-4cfd-a23c-0f749d654a78","label":"b","content":"Write down the mathematical name for shape **S**.","markscheme":"- Parallelogram B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Identifies the shape as a parallelogram.","code":"B"}],"finalAnswers":["Parallelogram"],"generatedAt":"2026-05-06T13:59:22.382Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"identify_properties","label":"Identify the shape's properties","steps":[{"type":"text","order":0,"title":"Recognise the property","content":"In shape $S$, both pairs of opposite sides are parallel. This is the defining property needed to classify the quadrilateral.","highlights":[{"text":"shape **S**","location":"specification"}]},{"type":"text","order":1,"title":"Name the shape","content":"A quadrilateral with both pairs of opposite sides parallel is a **parallelogram**. Writing **parallelogram** earns the B1 mark.","highlights":[{"text":"shape **S**","location":"specification"}]}]}],"generatedAt":"2026-07-19T15:29:38.136Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"cc0438d5-3c32-4e7e-a633-3110db525fae","label":"c","content":"Find the area of shape **S**.","markscheme":"- Applies area of a parallelogram formula: $\\text{base} \\times \\text{height} = 7 \\times 2$ M1\n- Final answer: $14$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Calculation and final area of parallelogram S.","code":"M"}],"finalAnswers":["14"],"generatedAt":"2026-05-06T13:59:22.382Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"parallelogram_area","label":"Base times perpendicular height","steps":[{"type":"text","order":0,"title":"Identify the formula","content":"Shape **S** is a parallelogram. Its area is found using\n\n$$\\text{

Area and Perimeter

Question 31

Area and Perimeter Questions

Area and Perimeter

Question 31

Area and Perimeter Questions