Worksheet 69: Area of composite shapes (Learning Number Level 2)

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Worksheet 69: Area of composite shapes

Worksheet 69

Learning Number Level 2

Area of composite shapes

To find areas of composite shapes with straight edges:

Example 1

¡ñ

split the shape into rectangles and triangles;

¡ñ

find the areas of the individual bits;

¡ñ

add or deduct the areas to get the total area.

We use formulae to calculate area.

breadth

RECTANGLE

Area = length ¡Á breadth

length

length

SQUARE

Area = length ¡Á length

Note

length and breadth

in same units

length

Keep the units the

same.

1

If a rectangle measures 5m by 3m, its area is 5 x 3 = 15 m2 (square

metres).

¡ñ

If a square is 12 mm along each side, its area is 12 x 12 = 144 mm2

(square millimetres).

See how all the measurements are in the same ¡®family¡¯ ¨C

nt

Hi

¡ñ

lengths in metres (m) give area in square metres (m2)

lengths in millimetres (mm) give area in square millimetres (mm2).

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Learning Number Level 2

Worksheet 69: Area of composite shapes

More complicated shapes can often be split into rectangles, like this:

10.5 m

C

Setting out is

3.5 m

it easier to total your

6m

important as it makes

A

2m

nt

Hi

3.8 m

B

individual areas and

find any mistakes.

3m

4m

Area A = 6 ¡Á 4 = 24 m2

Area B = 3.5 ¡Á 1.8 = 6.3 m2

Area C = 3 ¡Á 3.8 = 11.4 m2

Total area = A + B + C = 41.7 m2

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Worksheet 69: Area of composite shapes

Learning Number Level 2

Or we can treat them as larger rectangles with smaller rectangles or

squares removed, as below.

13 m

8.5 m

C

A

B

3m

3m

3.5 m

3.5 m

8.5 m

3m

3m

Shaded area = area of large rectangle ¨C (total area of A + B + C)

Area of large rectangle = 13 ¡Á 12 = 156 m2

Area A = 3 ¡Á 3.5 = 10.5 m2

Area B = 3 ¡Á 3.5 = 10.5 m2

Area C = 3 ¡Á 3 = 9 m2

Total area of A + B + C = 30 m2

Area of shaded area = 156 m2 ¨C 30 m2 = 126 m2

3

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Learning Number Level 2

Worksheet 69: Area of composite shapes

Make sketches of these diagrams and calculate the shaded areas.

Exercise 1

Where there are decimals in an answer, round the final answer to two

decimal places. In some cases, you may have to work out missing

measurements before you start.

3.10 m

1.82 m

0.71 m

4.00 m

1.94 m

2.41 m

3.62 m

2.91 m

3.10 m

1.68 m

2

4.71 m

1.21 m

1

4.00 m

2.89 m

3

4

12.2 m

7.3 m

4.6 m

3.4 m

5.8 m

2.3 m

3.1 m

11.8 m

3m

1m

5

6

11.5 m

6.5 m

5m

8m

12 m

8m

6m

2.4 m

5m

2.3 m

1m

3.1 m

1.8 m

2.8 m

3.2 m

3.1 m

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Worksheet 69: Area of composite shapes

Learning Number Level 2

Area of a triangle

Sometimes, the shapes might be triangular.

Example 2

It is quicker to work out the area of a triangle by this rule:

Area of triangle =

1

2

¡Á base ¡Á height

The base can be any side.

The height is the line from the base to the opposite corner.

Example:

Area of triangle

=

1

2

¡Á 10 ¡Á 3

=

1

2

¡Á 30

= 15 cm2

height

3 cm

base

10 cm

Exercise 2

1

Find the areas of these triangles.

(a)

(b)

12

2 cm

8 cm

5

cm

25

cm

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