Area and perimeter: past paper questions

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• Question 7May/June 2026, paper 12Structured3 marksHas a diagram

  The diagram shows a trapezium. All the lengths are in centimetres. The area of the trapezium is $100{\text{ cm}}^2$.

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• Question 24Oct/Nov 2025, paper 11Structured10 marks

  The diagram shows a rectangle and a triangle. The length of the rectangle is $x\text{ cm}$ and the area of the rectangle is $30{\text{ cm}}^2$. The triangle has sides of length $(x-1)\text{ cm}$, $(x+2)\text{ cm}$ and $(2x-3)\text{ cm}$.

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• Question 17Oct/Nov 2024, paper 12Structured4 marksHas a diagram

  The diagram shows a shaded triangle, $ABC$, drawn on a $1\mathrm{c}\mathrm{m}$ square grid. The equation of the line $AC$ is $y=-\frac{3}{2}x+1$. The shaded region inside triangle $ABC$ is defined by three inequalities.

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• Question 8Oct/Nov 2023, paper 22Structured9 marksHas a diagram

  The diagram shows a small rectangle inside a large rectangle. The height of the large rectangle is $x\text{ cm}$. The length of the large rectangle is 4 times its height.

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• Question 17May/June 2026, paper 12Structured9 marks

  In a right-angled triangle • the base is $x\text{ cm}$ • the height is $7\text{ cm}$ shorter than the base • the hypotenuse (longest side) is $2\text{ cm}$ longer than the base. Use this information to form an equation and show that it simplifies to $x^2-18x+45=0$.

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• Question 20May/June 2025, paper 22Structured9 marks

  $ABCD$ and $EFGD$ are rectangles. Show that $CD=x-1$.

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• Question 5May/June 2024, paper 12Structured3 marksHas a diagram

  In this question all dimensions are given in centimetres. The diagram shows a parallelogram. Find the perimeter of the parallelogram.

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• Question 21May/June 2023, paper 11Structured3 marksHas a diagram

  The diagram shows two rectangles. Rectangle $ABCD$ is mathematically similar to rectangle $PQRS$. $AB=12\text{ cm}$, $BC=9\text{ cm}$ and $PQ=8\text{ cm}$.

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• Question 3May/June 2026, paper 22Structured2 marksHas a diagram

  The diagram shows the net of a cuboid made from four congruent rectangles and two congruent squares. Find the total length of the edges of the cuboid.

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• Question 22May/June 2025, paper 22Structured9 marksHas a diagram

  The diagram shows a triangular field $ABC$. $AB=150\text{ m}$, $BC=187\text{ m}$ and angle $ABC={112}^{\circ }$. Fencing is needed for the perimeter of the field.

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• Question 20May/June 2026, paper 22Structured3 marks

  The area of a rectangle is $69.5{\text{ m}}^2$, correct to the nearest $0.5{\text{ m}}^2$. The width of the rectangle is $3.8\text{ m}$, correct to the nearest $0.1\text{ m}$. Calculate the upper bound of the length of the rectangle.

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• Question 22May/June 2026, paper 22Structured8 marksHas a diagram

  The diagram shows a triangular garden $ABD$. A path from $A$ meets $BD$ at point $C$. $CD=8\text{ m}$, angle $ADC={18}^{\circ }$, angle $ACB={34}^{\circ }$ and angle $ABC={90}^{\circ }$.

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