Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Area and perimeter

12 original questions, 36 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

A rectangle has length 9 cm and width 4 cm.

  1. Work out the area of the rectangle.
  2. Work out the perimeter of the rectangle.
2 marks
Show answer
a) 36 cm2 b) 26 cm
2

The diagram shows a parallelogram.

  1. Work out the area of the parallelogram.
  2. Work out the perimeter of the parallelogram.
  3. The parallelogram is cut along a diagonal into two identical triangles. Work out the area of one of the triangles.
9 cm6 cm5 cmDiagram NOT accurately drawn
3 marks
Show answer
a) 45 cm2 b) 30 cm c) 22.5 cm2
3
  1. A rectangular noticeboard has an area of 84 cm2 and a length of 12 cm. Work out the width of the noticeboard.
  2. A triangle has an area of 36 cm2 and a base of 9 cm. Work out the perpendicular height of the triangle.
3 marks
Show answer
a) 7 cm b) 8 cm
4
  1. Change 4 m2 to cm2.
  2. Change 2500 mm2 to cm2.
  3. Arjun says, "1 m2 is the same as 100 cm2." Explain why Arjun is wrong.
3 marks
Show answer
a) 40000 cm2 b) 25 cm2 c) open: 1 m2 is 100 cm by 100 cm, which is 10 000 cm2, not 100 cm2
5

The diagram shows a trapezium.

  1. Work out the area of the trapezium.
  2. Work out the perimeter of the trapezium.
12 cm5 cm9 cm4 cmDiagram NOT accurately drawn
3 marks
Show answer
a) 42 cm2 b) 30 cm
6

A trapezium has parallel sides of length 8 cm and 14 cm.

The area of the trapezium is 66 cm2.

Work out the perpendicular height of the trapezium.

2 marks
Show answer
6 cm
7

The shape is made from a rectangle and a right-angled triangle.

  1. Work out the perimeter of the shape.
  2. Work out the area of the shape.
6 cm4 cm10 cm12 cmDiagram NOT accurately drawn
4 marks
Show answer
a) 32 cm b) 48 cm2
8

A circle has radius 6 cm.

  1. Work out the circumference of the circle. Give your answer correct to 1 decimal place.
  2. Work out the area of the circle. Give your answer correct to 1 decimal place.
3 marks
Show answer
a) 37.7 cm b) 113.1 cm2
9

A circle has diameter 18 cm.

  1. Work out the circumference of the circle. Give your answer in terms of π.
  2. Work out the area of the circle. Give your answer in terms of π.
3 marks
Show answer
a) 18pi cm b) 81pi cm2
10

Shape A is a semicircle with diameter 10 cm.

Shape B is a quarter circle with radius 8 cm.

  1. Work out the perimeter of shape A. Give your answer correct to 1 decimal place.
  2. Work out the area of shape B. Give your answer in terms of π.
10 cm8 cmABDiagram NOT accurately drawn
4 marks
Show answer
a) 25.7 cm b) 16π cm2
11

A sector of a circle has radius 7.5 cm and angle 140°.

  1. Work out the arc length of the sector.
  2. Work out the area of the sector.

Give each answer correct to 3 significant figures.

4 marks
Show answer
a) 18.3 cm b) 68.7 cm²
12

A sector of a circle has radius 6 cm and area 15π cm².

Work out the angle of the sector.

2 marks
Show answer
150°

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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