Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Area of compound shapes

Splitting shapes into rectangles and triangles.

17 original questions, 65 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

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
2

A rectangle is 12 cm long and 9 cm wide.

A rectangle 5 cm by 4 cm is removed from one corner.

Work out the area of the remaining shape.

12 cm5 cm4 cm9 cmDiagram NOT accurately drawn
3 marks
Show answer
88 cm²
3

A square of side 6 cm and a square of side 3 cm are joined to make a shape. The small square sits on top of the large square, with their left-hand edges in line.

  1. Work out the perimeter of the shape.
  2. Work out the area of the shape.
3 marks
Show answer
a) 30 cm b) 45 cm²
4

The front of a shed is made from a rectangle with a triangle on top.

The rectangle is 10 cm wide and 6 cm high in a scale drawing. The triangle sits exactly on top of the rectangle, with base 10 cm and perpendicular height 4 cm.

Work out the total area of the scale drawing.

10 cm6 cm4 cmDiagram NOT accurately drawn
4 marks
Show answer
80 cm²
5

A T-shape is made from two rectangles. The top bar is 12 cm long and 3 cm wide. The stem is 4 cm wide and 6 cm long. It is joined to the middle of the lower edge of the bar and hangs straight down.

  1. Work out the perimeter of the T-shape.
  2. Work out the area of the T-shape.
4 marks
Show answer
a) 42 cm b) 60 cm²
6

A flower bed is a square of side 8 m. A quarter circle of radius 3 m is cut out of one corner and paved. The rest of the square is planted with grass.

Work out the area of grass. Give your answer correct to 1 decimal place.

3 marks
Show answer
56.9 m²
7

ABCD is a trapezium with AB parallel to DC. Angle A and angle D are both 90°. AB = 9 cm, DC = 15 cm and BC = 10 cm. The area of the trapezium is 96 cm².

  1. Work out the length AD.
  2. Work out the perimeter of ABCD.
3 marks
Show answer
a) 8 cm b) 42 cm
8

Two identical squares, each with sides of length 6 cm, overlap.

The overlapping region is a square with sides of length 2 cm.

Work out the total area covered by the two squares.

6 cm6 cm2 cmDiagram NOT accurately drawn
4 marks
Show answer
68 cm²
9

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
10

Square P has side 10 cm. Square Q has side 7 cm. The squares overlap so that they share a 4 cm by 4 cm square.

  1. Work out the area of the part of square Q that is outside square P.
  2. Work out the total area covered by the two squares together.
3 marks
Show answer
a) 33 cm² b) 133 cm²
11

A window is a rectangle with a semicircle on top. The rectangle is 1.2 m wide and 1.5 m high. The diameter of the semicircle is the 1.2 m width of the rectangle.

Glass costs £40 per m².

  1. Work out the area of the window. Give your answer correct to 2 decimal places.
  2. Work out the cost of the glass, to the nearest pound.
4 marks
Show answer
a) 2.37 m² b) £95
12

The end wall of a loft is a trapezium. The parallel sides are 5.2 m and 3.4 m long and they are 2.5 m apart. Isabel will cover the wall with cladding. Each pack covers 2 m² and costs £14.50.

  1. Work out the area of the wall.
  2. How many packs must Isabel buy, and what will they cost?
  3. Write down one assumption you made in part (b).
4 marks
Show answer
a) 10.75 m² b) 6 packs, £87 c) Assume there is no waste when cutting the cladding (in practice she should buy extra)
13

The diagram shows the floor of a workshop. The floor is an L-shape made from a rectangle 7 m by 4 m joined to a rectangle 3 m by 2 m.

Marco is going to paint the whole floor. One tin of floor paint covers 8 m² and costs £22.

Work out the total cost of the tins of paint Marco needs to buy.

2 m3 m2 m7 m4 m7 m3 mDiagram NOT accurately drawn
5 marks
Show answer
£110
14

A rectangular garden is 9 m long and 7 m wide.

A rectangular patio 4 m by 3 m is laid inside the garden. The rest of the garden is to be covered with grass seed.

One bag of grass seed covers 15 m² and costs £9.99.

Work out the total cost of the bags of grass seed needed.

5 marks
Show answer
£39.96
15

A field is made from a rectangle 60 m by 40 m joined along one 40 m side to a right-angled triangle. The triangle has base 40 m and perpendicular height 30 m.

Fertiliser for the field costs 5p per square metre.

Work out the total cost of the fertiliser. Give your answer in pounds.

60 m40 m40 m60 m30 mDiagram NOT accurately drawn
5 marks
Show answer
£150
16

Two identical squares are cut from a rectangular sheet of card 14 cm long and 10 cm wide. The squares do not overlap.

The area of the card remaining is 90 cm².

Work out the side length of each square.

5 marks
Show answer
5 cm
17

The end wall of a barn is a trapezium. The parallel sides of the trapezium are 6 m and 8 m long, and the perpendicular distance between them is 3 m.

Priya is going to paint the wall. One tin of paint covers 5 m² and costs £13.50.

Work out the total cost of the tins of paint Priya needs to buy.

5 marks
Show answer
£67.50

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 4 topics