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1.035 Area of composite shapes

Worksheet
Composite shapes
1

Find the area of the shaded region in the following diagrams:

a
b
c
d
e
f
g
h
2

Find the area of the following composite shapes:

a
b
c
d
e
f
g
h
i
j
k
l
3

The quadrilateral in the diagram has a diagonal measuring 14\text{ m}.

Calculate the total area of the quadrilateral.

4

Find the area of the figure, correct to two decimal places.

All dimensions are in \text{mm}.

5

Find the area of the following composite shapes, to two decimal places:

a
b
c
d
6

Find the area of the shaded region in the following figures, correct to one decimal place:

a
b
c
d
e
f
g
h
i
j
7

Find the area of the shaded region in the following figures, correct to two decimal places:

a
b
Applications
8

Luke wants to wallpaper two walls each measuring 3.9 metres high and 9.75 metres wide. One of the walls includes a doorway 0.8 metres wide and 1.6 metres high.

a

Find the total area to be wallpapered.

b

If each roll of wallpaper will cover an area of 10\text{ m}^2, how many full rolls must Luke buy to cover the entire wall.

9

Lachlan draws the plot of land which contains his house and garden.

a

Find the total area of the plot of land.

b

Find the area covered by the house.

10

A quilt is made by sewing together 4 identical parallelograms as shown in the following figure:

If the total area of the quilt is 1944\text{ cm}^2, calculate the perpendicular height of each parallelogram piece.

11

Tricia is drawing a yin-yang symbol. She chooses to make the radius of the overall circle be 16 \,\text{cm} and the radius of the small circles be 2 \,\text{cm}:

Find the area of the shaded part of the symbol.

Round your answer to two decimal places.

12

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 kg of fertiliser to fertilise 100 square metres, how many kilograms of fertiliser should the farmer purchase?

13

The back cover of a mobile phone is shown in the following diagram. The rounded corners are quadrants:

Find the area of the back cover, excluding the circular camera lens. Round your answer to two decimal places.

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Outcomes

3.1.3

determine the area of composite figures by decomposition into familiar shapes

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