Robinson Tuition
Year 7 · 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

Write down the mathematical name of a polygon with exactly five sides.

1 mark
Show answer
pentagon
2

Here are four polygons, A, B, C and D.

For each polygon, write down its name and whether it is regular or irregular.

ABCD
4 marks
Show answer
A) regular hexagon B) irregular pentagon C) regular (equilateral) triangle D) irregular hexagon
3

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
4
  1. A regular octagon has sides of length 7 cm. Work out its perimeter.
  2. Work out the perimeter of the pentagon in the diagram.
  3. A regular hexagon has a perimeter of 45 cm. Work out the length of one side.
8 cm4 cm5.5 cm5 cm3.5 cmDiagram NOT accurately drawn
3 marks
Show answer
a) 56 cm b) 26 cm c) 7.5 cm
5

A triangle has base 12 cm and perpendicular height 5 cm.

Work out the area of the triangle.

2 marks
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30 cm²
6

The diagram shows a parallelogram A and a trapezium B.

  1. Work out the area of parallelogram A.
  2. Work out the area of trapezium B.
9 cm5 cm10 cm6 cm4 cm5 cmABDiagram NOT accurately drawn
4 marks
Show answer
a) 36 cm² b) 40 cm²
7

An L-shape is made by joining a rectangle 8 cm by 5 cm to a rectangle 4 cm by 3 cm. The two rectangles do not overlap.

Work out the total area of the L-shape.

8 cm5 cm3 cm4 cmDiagram NOT accurately drawn
2 marks
Show answer
52 cm²
8

An L-shape is made by removing a rectangle 3 cm by 2 cm from one corner of a rectangle 8 cm by 6 cm.

Work out the perimeter of the L-shape.

8 cm3 cm2 cm6 cmDiagram NOT accurately drawn
3 marks
Show answer
28 cm
9

The diagram shows a shape made from rectangles. All the corners are right angles.

  1. Work out the perimeter of the shape.
  2. Work out the area of the shape.
12 cm5 cm7 cm9 cmDiagram NOT accurately drawn
4 marks
Show answer
a) 42 cm b) 88 cm²
10

A rectangle is made from three identical squares placed side by side in a row.

The perimeter of the rectangle is 48 cm.

Work out the area of the rectangle.

3 marks
Show answer
108 cm²
11

Kemi's bedroom floor is a rectangle 4.5 m long and 3.2 m wide.

Carpet costs £12.50 per square metre. Carpet can only be bought in whole square metres.

Work out the cost of carpet for the floor.

4 marks
Show answer
£187.50
12

A school lawn is in the shape of a trapezium.

The parallel sides are 8 m and 14 m long. The perpendicular distance between them is 6 m.

The caretaker is going to sow grass seed on the whole lawn. One box of grass seed covers 20 m2 and costs £8.75.

Work out the cost of the grass seed.

4 marks
Show answer
£35

Your score

Answer the questions above and your score appears here.

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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