Area and perimeter: past paper questions

Where the questions come from

• Question 4May/June 2026, paper 21Structured2 marks

  The diagram shows a rectangle with width $6\text{ cm}$. The width of the rectangle is $\frac{1}{12}$ of the perimeter of the rectangle. Work out the length of the rectangle.

  Try this question
• Question 4Oct/Nov 2025, paper 21Structured2 marks

  The area of a triangle is $12{\text{ cm}}^2$. The length of the base of the triangle is $8\text{ cm}$. Work out the height of the triangle.

  Try this question
• Question 6Oct/Nov 2024, paper 22Structured2 marksHas a diagram

  The diagram shows a trapezium. The area of the trapezium is $42{\text{ cm}}^2$. Calculate the value of $x$.

  Try this question
• Question 2May/June 2026, paper 22Structured5 marks

  The diagram shows an accurate net of an open box in the shape of a cuboid. All the dimensions are whole numbers of centimetres. Find the total area of the net.

  Try this question
• Question 4Oct/Nov 2025, paper 23Structured2 marksHas a diagram

  A rectangle measures $5\text{ cm}$ by $19\text{ cm}$. Two of these rectangles are joined to make a shape. Work out the perimeter of the shape.

  Try this question
• Question 9Oct/Nov 2024, paper 22Structured3 marks

  Points $A$, $B$, $C$ and $D$ lie on a circle. $ABCD$ is a square with area $72{\text{ cm}}^2$. Calculate the area of the circle.

  Try this question
• Question 18May/June 2026, paper 23Structured6 marksHas a diagram

  The diagram shows a rectangle. The shaded area is $30{\text{ cm}}^2$. Show that $x^2+16x-36=0$.

  Try this question
• Question 7Oct/Nov 2025, paper 42Structured8 marksHas a diagram

  The diagram shows a parallelogram. The parallelogram has the same perimeter as a circle with radius 4 m. Show that $x=6.06\text{ m}$, correct to 2 decimal places.

  Try this question
• Question 6Oct/Nov 2024, paper 41Structured11 marksHas a diagram

  The diagram shows a field $ABCD$. A straight path $AC$ goes across the field. Show that $AC=1028\text{ m}$, correct to the nearest metre.

  Try this question
• Question 6May/June 2026, paper 42Structured3 marks

  A semicircle has a diameter of $15.8\text{ cm}$. Calculate the perimeter of the semicircle.

  Try this question
• Question 15Oct/Nov 2025, paper 42Structured10 marks

  The diagram shows a field, $ABCD$, in the shape of a quadrilateral. $BD$ is a straight path across the field. Calculate $BC$.

  Try this question
• Question 10Oct/Nov 2024, paper 41Structured14 marksHas a diagram

  This rectangle has area $190{\text{ cm}}^2$. By forming and solving an equation, show that $x=8.5$.

  Try this question
• Question 18May/June 2026, paper 42Structured8 marks

  In this question, all lengths are in centimetres. Show that the area of triangle $ABC$ is $\frac{1}{2}{x}^2{\text{ cm}}^2$.

  Try this question
• Question 4May/June 2025, paper 42Structured2 marksHas a diagram

  $ABCD$ is a trapezium. Work out the area of the trapezium.

  Try this question
• Question 7Oct/Nov 2024, paper 42Structured20 marksHas a diagram

  The diagram shows a field, $ABCD$ with $B$ north of $A$. $BD$ is a path across the field. $AB=85\text{ m}$, $AD=72\text{ m}$, $BD=129\text{ m}$, angle $BDC={39}^{\circ }$ and angle $BCD={60}^{\circ }$.

  Try this question
• Question 12May/June 2025, paper 42Structured2 marks

  The length of a rectangle is $16\text{ cm}$, correct to the nearest centimetre. The width of the rectangle is $14\text{ cm}$, correct to the nearest centimetre. Calculate the lower bound of the perimeter of the rectangle.

  Try this question
• Question 7Oct/Nov 2024, paper 43Structured15 marksHas a diagram

  Calculate the area of the trapezium.

  Try this question
• Question 20May/June 2025, paper 42Structured13 marksHas a diagram

  The diagram shows a quadrilateral $ABCD$. $CD=10\text{ m}$ and $DB=12\text{ m}$. Angle $DBA={90}^{\circ }$, angle $CDB={56}^{\circ }$ and angle $ADB={34}^{\circ }$.

  Try this question
• Question 12Oct/Nov 2024, paper 43Structured10 marksHas a diagram

  $ABCD$ is a quadrilateral and $E$ is a point on $CD$. $AB=8.7\text{ cm}$, $BC=11.4\text{ cm}$ and $CE=10.9\text{ cm}$. Angle $ADE={90}^{\circ }$, angle $ABC={119}^{\circ }$ and angle $CAE={20}^{\circ }$.

  Try this question
• Question 4May/June 2025, paper 43Structured3 marksHas a diagram

  The diagram shows a pentagon made from two congruent trapeziums. The area of the pentagon is $130.2{\text{ cm}}^2$. Calculate the value of $x$.

  Try this question
• Question 4May/June 2024, paper 43Structured9 marks

  In this question all the measurements are in centimetres. The area of the triangle is equal to the area of the square. Show that $3r^2+r-6=0$.

  Try this question