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4.045 Composite areas

Worksheet
Area of composite shapes
1

Consider the following figure:

a

Find the area of rectangle B.

b

Find the total area of the given shape.

2

For the following composite shape:

a

Find the area of rectangle A.

b

Find the total area of the given shape.

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 following composite shapes:

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

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

a
b
c
d
e
f
7

Consider the following figure:

a

Find the value of x.

b

Find the area of the shaded region.

Applications
8

The lounge room floor shown is to be tiled with slate tiles. The cost of tiling the room is \$25/\text{m}^2.

a

Find the area to be tiled.

b

How much will it cost to tile the room?

9

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

Find the area of the garden bed.

10

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.

11

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

1.3.8

calculate areas of rectangles and triangles, and composites of these shapes

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