4.05 Area of shapes

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

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

Find the area of the following squares:

For the following figures:

a

b

c

Find the area of the following triangles:.

a

b

c

d

e

f

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

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.

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

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

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.

Find the area of the following parallelograms:

a

b

c

d

e

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

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

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

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

a

b

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

Find the area of the following trapeziums:

a

b

c

d

e

f

g

h

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

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.

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?

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.

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?

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.

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?

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}.