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Australia
Year 8

8.05 Composite shapes

Worksheet
Perimeter of composite shapes
1

For each of the following composite shapes:

i

State the basic shapes that make up the composite shape.

ii

Find the perimeter.

a
b
c
d
e
2

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

a
b
c
d
e
Area of composite shapes
3

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

a
b
c
d
e
f
g
h
i
j
k
l
4

Find the exact shaded area of the following figures:

a
b
c
d
e
f
5

For each of the following composite shapes:

i

State the basic shapes that make up the composite shape.

ii

Find the exact area.

a
b
6

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.

Applications
7

A piece of origami paper, orginally in the shape of a parallelogram, is folded along its shortest diagonal as shown.

What is the total area covered by the folded paper?

8

Lachlan designs a plot of land which contains his house and garden as shown in the diagram:

a

Find the total area of the plot of land.

b

Find the area of the garden.

9

The figure shows a plan of a dining room floor, which is to be tiled with slate tiles.

a

Calculate the area to be tiled. Round your answer to the nearest metre squared.

b

If the cost of tiling is \$10/m^2, how much will it cost to tile the dining room floor?

10

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

ACMMG196

Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites

ACMMG197

Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area

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