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14.07 Composite shapes

Worksheet
Composite shapes
1

For each of the following figures:

i

Find the area of rectangle B.

ii

Find the total area of the composite shape.

a
b
2

For the following composite shape:

a

Find the area of rectangle A.

b

Find the total area of the given shape.

3

Find the area of the following composite shapes:

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

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

Calculate the total area of the quadrilateral.

Holes and cutaways
5

Consider the following figures, where all measurements are in centimetres:

  • Figure 1:

  • Figure 3:

  • Figure 2:

  • Figure 4:

a

Find the area of the entire rectangle shaded as shown in figure 1.

b

Find the area of the interior rectangle shaded as shown in figure 2.

c

Find the area of the corner rectangle shaded as shown in figure 3.

d

Hence, calculate the area of the shaded region as shown in figure 4.

6

Consider the following figures:

  • Figure 1:

  • Figure 2:

a

Find the area of the shaded rectangle as shown in figure 1.

b

Find the area of the shaded triangle as shown in figure 2.

c

Hence, find the area of the shaded region as shown in figure 3.

  • Figure 3:

7

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

a
b
c
d
e
f
8

Consider the following figure:

a

Find the value of x.

b

Find the area of the shaded region.

9

For each of the following figures:

i

Find the value of x.

ii

Find the value of y.

iii

Calculate the area of the shaded region.

a
b
10

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

a
b
Applications
11

Katrina has a garden bed that is shaped as shown in the following figure:

Find the area of the garden bed.

12

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.

13

The dining room floor shown is to be tiled with slate tiles. The cost of tiling the room is \$10 per square metre.

a

Calculate the area to be tiled.

b

How much will it cost to tile the room?

14

A piece of paper in the shape of a parallelogram is folded along its shortest diagonal, as shown. Find the total area covered by the folded paper.

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

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Outcomes

MA4-13MG

uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area

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