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Area and perimeter questions and answers

Perimeter is the distance around a shape; area is the space inside it. Rectangle: length × width. Triangle: 12×\tfrac{1}{2} \times base × height. Parallelogram: base × height. Trapezium: 12(a+b)h\tfrac{1}{2}(a + b)h. The height is always measured at right angles to the base.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated .

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Where area and perimeter comes up

GCSE (AQA, Edexcel, OCR)Foundation and Higher: know and apply formulae for the area of triangles, parallelograms and trapezia, and calculate perimeters and areas of composite shapes.
Cambridge IGCSE (0580)Core and Extended: perimeter and area of a rectangle, triangle, parallelogram and trapezium (only the triangle formula is given).

The method

  1. Pick the right formula for the shape.
  2. Use the perpendicular height, not the slanted side.
  3. Compound shapes: split into rectangles and triangles, or subtract a missing piece.
  4. Working backwards: put the area into the formula and solve.

Area and perimeter questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

Find the area of a rectangle 8 cm long and 5 cm wide.

Question 2Warm-upFoundation

Find the area of a triangle with base 10 cm and height 6 cm.

Exam-style

Question 3Exam-styleFoundation

Find the area of a parallelogram with base 12 cm and perpendicular height 7 cm.

Question 4Exam-styleFoundation

A trapezium has parallel sides 6 cm and 10 cm, and height 5 cm. Find its area.

Question 5Exam-styleFoundation

A 10 cm by 6 cm rectangle has a 4 cm by 3 cm rectangle cut from one corner. Find the area of the shape left.

Question 6Exam-styleFoundation

A rectangle has area 72 cm² and width 6 cm. Find its perimeter.

Challenge

Question 7ChallengeFoundation

A square has a perimeter of 36 cm. Find its area.

Question 8ChallengeFoundation

A triangle has area 24 cm² and base 8 cm. Find its height.

Common mistakes

  • Using the slanted side as the height.
  • Forgetting to halve for a triangle or trapezium.
  • Mixing up area (cm²) and perimeter (cm).

Stuck on one of these?

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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