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4.07 Area of composite shapes

Worksheet
Area of composite shapes
1

Consider the figure below:

a

Find the area of rectangle B.

b

Calculate the total area of the composite shape.

2

Find the area of the following figures:

a
b
c
d
e
f
g
h
3

Find the shaded area of the following figures:

a
b
c
d
e
f
g
h
4

Find the shaded area of the following figures:

a
b
c
d
5

For each of the following figures:

i

Find the value of x.

ii

Find the area of the shaded region.

a
b
6

Find the area of the following figure. All dimensions are in metres.

7

Find the area of the figure shown. All dimensions are in millimetres.

8

For each of the following figures:

i

Find the value of x.

ii

Find the value of y.

iii

Find the area of the shaded region.

a
b
9

Find the shaded area of the following figures:

a
b
10

Find the area of the following figures:

a
b
c
d
e
f
g
11

Find the area of the following figures, to one decimal place:

a
b
c
d
e
f
g
h
i
12

Find the shaded area of the following figures. Round your answers to one decimal place.

a
b
c
d
e
f
g
h
Applications
13

A circular metal plate of diameter 2 metres, has 65 holes of diameter 5\text{ cm} drilled into it. Find the remaining area of the metal plate in square metres. Round your answer to two decimal places.

14

Luke wants to wallpaper two walls each measuring 3.9 \text{ m} high and 9.75 \text{ m} wide. One of the walls includes a doorway measuring 0.8 \text{ m} wide and 1.6 \text{ m} high.

a

Find the total area to be wallpapered.

b

If each roll of wallpaper covers an area of 10 \text{ m}^{2}, calculate the number of full rolls Luke must buy to cover the entire area.

15

A farmer is going to fertilise his paddock, which has the following shape:

a

Find the area of the paddock.

b

If it takes 150\text{ kg} of fertiliser to fertilise 100 square metres, how many kilograms of fertiliser should the farmer purchase?

16

The bath room floor shown is to be tiled with slate tiles. The cost of tiling the room is \$15 per square metre.

a

Calculate the area to be tiled.

b

How much will it cost to tile the room?

17

The design attached is made using a large circle and 2 smaller circles of diameter 3\text{ cm}. Find the area of the shaded region correct to one decimal place.

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Outcomes

MS11-4

performs calculations in relation to two-dimensional and three-dimensional figures

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