 4.05 Area of shapes

Worksheet
Area of rectangles
1

Find the area of the rectangle shown:

2

Find the area of a rectangle whose length is 12 \text{ cm} and width is 5 \text{ cm}.

3

If the area of a rectangle is 99 \text{ cm}^2 and its width is 9 \text{ cm}, find its length.

4

Find the area of the square shown.

5

Find the area of the following squares:

a

whose side is 5 \text{ cm}

b

whose perimeter is 8 \text{ cm}

Area of triangles
6

For the following figures:

i

Find the area of the entire rectangle.

ii

Hence, find the area of the triangle.

a
b
c
7

Find the area of the following triangles:.

a
b
c
d
e
f
8

Find the area, A, of a triangle with base, b, of 6 \text{ m} and height, h, of 12 \text{ m}.

9

For each of the following triangles, find the value of the pronumeral using the given area:

a

Area = 54 \text{ cm}^2.

b

Area = 120 \text{ cm}^2

c

Area = 120 \text{ mm}^2.

d

Area = 24 \text{ m}^2.

e

Area = 12 \text{ mm}^2.

10

Find the base of the triangle whose area is 17.5\text{ cm}^2 and height is 5 \text{ cm}.

11

The following table shows measurements for three different triangles that all have an area of 42\text{ cm}^2.

Find the value of:

a
A
b
B
c
C
12

What could be the dimensions of a triangle with an area of 27\, \text{mm}^{2} ?

Area of parallelograms
13

For the following parallelogram:

a

If the parallelogram is formed into a rectangle, find:

i

The length of the rectangle.

ii

The width of the rectangle.

b

Find the area of the parallelogram.

14

Find the area of the following parallelograms:

a
b
c
d
e
15

Find the area of a parallelogram whose base is 15 \text{ cm} and height is 7 \text{ cm}.

16

Find the value of h in the parallelogram if its area is 35 \text{ m}^2.

17

Find the base length of a parallelogram whose area is 108\text{ cm}^2 and perpendicular height is 9\text{ cm}.

18

Find the perpendicular height of a parallelogram whose area is 99\text{ m}^2 and base is 9\text{ m}.

Area of trapeziums
19

Consider the two identical trapeziums that are placed to make the folowing parallelograms:

i

Find the area of the entire parallelogram.

ii

Find the area of one of the trapeziums.

a
b
20

Consider the two identical trapeziums that are used to make the following rectangle:

a

Find the area of the entire rectangle.

b

Find the area of one of the trapeziums.

21

Find the area of the following trapeziums:

a
b
c
d
e
f
g
h
22

For each of the following trapeziums, find the value of the pronumeral using the given area:

a

Area =24 \text{ cm}^2

b

Area =30 \text{ cm}^2

c

Area = 36 \text{ cm}^2

d

Area = 30 \text{ cm}^2

e

Area = 20 \text{ mm}^2

f

Area =36 \text{ cm}^2

g

Area =65 \text{ cm}^2

h

Area =30 \text{ mm}^2

Applications
23

The faces on a 4 sided die are all triangular. Each face has a base length of 13 \text{ mm} and a perpendicular height of 20 \text{ mm}. Find the area of one face of the die.

24

Sharon has purchased a rectangular piece of fabric measuring 12\text{ m} in length and 7\text{ m} in width. What is the area of the largest triangular piece she can cut out from it?

25

A harbour has a trapezoidal pier with a perpendicular height of 8 \text{ m}. One base of the pier has a length of 9 \text{ m} and the other has a length of 5 \text{ m}.

Find the area of the pier.

26

A gutter running along the roof of a house has a cross-section in the shape of a triangle.

If the area of the cross-section is 50 \text{ cm}^2, and the length of the base of the gutter is 10 \text{ cm}, find the perpendicular height h of the gutter in metres.

27

Deep sea divers are scanning an area of the sea bed where a boat capsized. They want to get to point P, which is h metres above the sea bed.

At this point, they can cast a light out to view 9 metres across the sea bed and a cross sectional area of 45 \text{ m}^2 of water. From side-on, the light casts a shape that looks like the diagram below. The divers descend at a rate of 1.2 metres per second.

a

Find h, the distance of the divers from the sea bed at the point P.

b

If the divers were descending directly downwards, how high above the sea bed were they 6 seconds before they reached point P?

28

At the entrance of the Louvre museum is a glass structure in the shape of a square base pyramid.

A replica of this pyramid is to be built such that each triangular face of the pyramid measures 7.5 metres at the base, and has a perpendicular height of 10 metres.

The faces will be made up of identical triangular glass tiles tessellated to fit exactly on each face.

a

Find the total area that needs to be covered with the triangular glass tiles.

b

How many glass tiles will be needed in total if each triangular tile measures 15 \text{ cm} across the base and has a perpendicular height of 20 \text{ cm}?

29

Some car parks require the cars to park at an angle as shown. The dimensions of the car park are as given, where each individual parking space has a length of 5.1\text{ m} and a width of 3.9\text{ m}. What area is needed to create an angled car park suitable for 7 cars?

30

The tile pattern shown is made up of two different parallelograms in a tessellated pattern.

a

Find the area covered by the smaller tiles.

b

Find the area covered by the larger tiles.

c

Calculate the total area covered.

31

A roof in the shape of a parallelogram is to be entirely covered by identical solar panels that are also in the shape of a parallelogram. Each solar panel measures 1.2\text{ m} along the longest side and has a perpendicular height of 0.6\text{ m}.

a

Find the area covered by one solar panel.

b

Find the number of solar panels to be installed if the roof measures 23.04\text{ m}^2 in area, and no part of the roof is to be left uncovered by solar panels.