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2.035 Area of composite shapes

Worksheet
Composite shapes
1

Find the area of the following composite shapes:

a
b
c
d
e
f
g
h
i
j
k
l
2

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

Calculate the total area of the quadrilateral.

3

Consider the following figure:

a

Find the value of x.

b

Find the area of the shaded region.

4

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

All dimensions are in \text{mm}.

5

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

a
b
c
d
e
f
g
h
6

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

a
b
c
d
7

Find the area of the shaded region of the image. Any curved shape is part of a circle.

Give your answer correct to two decimal places.

Note: the diagram is not to scale.

8

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
9

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

a
b
Applications
10

The dining room floor shown is to be tiled with slate tiles. The cost of tiling the room is \$10 / \text{ m}^{2}.

a

Calculate the area to be tiled.

b

How much will it cost to tile the room?

11

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.

12

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.

13

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?

14

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.

15

A simple t-shirt pattern has the dimensions given in the diagram below, with a semicircular neck hole in the front piece only.

a

If the front and back pieces are each cut from two rectangular pieces of fabric with dimensions 90 \text{ cm} by 80 \text{ cm}, how much fabric is wasted?

Give your answer in square centimetres.

b

The fabric costs \$8 per metre length, where a metre length is a piece of fabric with width 80 \text{ cm} and length 100 \text{ cm}. If the t-shirt pieces are cut out of two 0.9 metre lengths as in part (a), how much will the fabric cost for 100 t-shirts?

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Outcomes

3.1.3.2

estimate the areas of different shapes

3.1.3.3

use formulas to calculate areas of regular shapes, including triangles, squares, rectangles, parallelograms and circles

3.1.3.4

use formulas to calculate areas of regular shapes, including trapeziums and sectors [complex]

3.1.3.5

use formulas to calculate areas of composite figures by decomposing them into regular shapes [complex]

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