topic badge

10.06 Area of 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?

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

VCMMG258

Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving

What is Mathspace

About Mathspace