lar height is twice the length of the base. This means:\n\n$$\\text{base} \\times \\text{height} = 18$$","highlights":[{"text":"The perpendicular height of a parallelogram is twice the length of its base.","location":"specification"},{"text":"The area of the parallelogram is 18\\text{ cm}^2$.","location":"specification"}]},{"type":"text","order":1,"title":"List factors of 18","content":"Using **trial and improvement**, we can list the integer factor pairs of $18$ to see which pair satisfies our condition that the height must be twice the base:\n\n* **Pair 1:** $1 \\times 18 = 18$\n * Is $18$ twice of $1$? No, $18 = 18 \\times 1$.\n* **Pair 2:** $2 \\times 9 = 18$\n * Is $9$ twice of $2$? No, $9 = 4.5 \\times 2$.\n* **Pair 3:** $3 \\times 6 = 18$\n * Is $6$ twice of $3$? **Yes!** Since $2 \\times 3 = 6$, this pair meets the condition."},{"type":"text","order":2,"title":"Identify the final dimensions","content":"From our trial and improvement, we have successfully found the dimensions:\n\n* $$\\text{Base} = 3\\text{ cm}$$\n* $$\\text{Height} = 6\\text{ cm}$$\n\nThis earns the first method mark M1."},{"type":"text","order":3,"title":"Draw on the grid","content":"Now, we draw the parallelogram on the centimetre grid:\n\n1. Draw a horizontal straight line of length **$3\\text{ cm}$** (which is 3 grid squares) to act as the base.\n2. Count up **$6\\text{ squares}$** (for the vertical perpendicular height of $6\\text{ cm}$).\n3. Move slightly to the right or left to create the slant, and draw another parallel horizontal line of length **$3\\text{ cm}$**.\n4. Connect the ends of the two lines to complete your parallelogram.\n\nCompleting the drawing correctly earns the final accuracy mark A1."}]}],"generatedAt":"2026-06-12T14:58:47.567Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null},{"id":"4d85da44-7606-4a1d-a0d8-c92a790b16e9","revisionId":"ed574902-a384-4c5d-b95c-33bf587735cf","questionNumber":null,"questionType":"LA","specification":"Here is a rectangular piece of cardboard.\n\n![A rectangle with side lengths 10 cm and 4 cm.](https://assets.mathsgenie.co.uk/questions/d03dd016-8845-4b63-8d79-6f66f9887823.png)\n\nThe six-sided shape below is made from two of these pieces of cardboard.\n\n![A six-sided shape made from two 10 cm by 4 cm rectangles.](https://assets.mathsgenie.co.uk/questions/b578dd65-ffc1-4443-a8c4-0c372cc349cf.png)","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"3254ed80-fc5a-4499-b69a-477993104bd3","label":"a","content":"Work out the perimeter of this six-sided shape.","markscheme":"- Identifies missing vertical length: $10 - 4 = 6$ M1\n- Sums all outer sides: $10 + 4 + 10 + 4 + 10 + 6 + 4$ M1\n- Final answer: $48$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Identifies the missing length by finding the difference between the long and short side ($10 - 4 = 6$).","code":"M"},{"id":"p2","marks":1,"description":"Sums all the outer side lengths of the composite shape ($10 + 14 + 4 + 10 + 6 + 4$ or equivalent).","code":"M"},{"id":"p3","marks":1,"description":"Provides the correct final perimeter of 48 cm.","code":"A"}],"finalAnswers":["48"],"generatedAt":"2026-05-06T13:59:20.561Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"perimeter","label":"Find the perimeter","steps":[{"type":"text","order":0,"title":"Find the missing side","content":"The full left-hand vertical length is $10\\text{ cm}$. The lower vertical section is $4\\text{ cm}$, so the missing vertical section is\n$$10-4=6\\text{ cm}$$\nThis identifies the missing length, earning the first method mark.","highlights":[{"text":"Work out the perimeter of this six-sided shape.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=outer_sum}{\\color{@sky}{P=(10+4+10+4+10+6+4)\\text{ cm}}}$"},{"latex":"$$\\htmlData{anchor

Area and Perimeter

Question 16

Area and Perimeter Questions

Area and Perimeter

Question 16

Area and Perimeter Questions