1. Module 4

1.9. Page 4

Mathematics 10-3 Module 4 Lesson 2

Module 4: Area

 

Bringing Ideas Together

 

In the Explore you discovered how to use formulas to determine the area of a parallelogram and the area of a triangle.

  • area of a parallelogram = base × height, or
  • area of a triangle

Example 1

 

This photograph shows a square cloth folded in two to make a triangle.

A 30-in square cloth is folded along the diagonal to make two triangles. What is the area of each triangle?

 

Solution

 

This illustration shows a triangle with a base of 30 inches and a height of 30 inches.

 

b = 30 in

h = 30 in

 

 

The area of each triangle is 450 in2.

 

Example 2

 

A snake’s skin is covered with small parallelograms.

 

This photograph shows the small parallelogram pattern on a snake’s skin.

© Sergej Razvodovskij/shutterstock

 

One of the small parallelograms is pictured as follows.

 

 

 

This illustration shows a parallelogram with a base of 3 millimetres and a height of 2.5 millimetres.

 

What is the area of this parallelogram?

 

Solution


b = 3 mm

h = 2.5 mm

 

 

The area of the parallelogram is 7.5 mm2.

 

Example 3

 

Find the area of the following triangle.

 

 

 

This illustration shows a triangle with a base of 1 foot and a height of 6 inches.


Solution

 

Each side must be expressed in the same units. Remember that 1 ft = 12 in.

 

 

 

b = 1 ft = 12 in

h = 6 in

 

 

So,

 

 

 

 

The area of the triangle is 36 in2.

 

Now practise your skill in finding area.

 

Self-Check

Answer the following questions. When you are finished, check your answers.

 

SC 2. A bedspread is turned down as shown.

 

This illustration shows a turned-down bedspread displaying a triangle of size 3 feet by 4 feet by 5 feet.

 

What is the area of the triangular portion?

 

SC 3. A railroad crosses a highway as shown.

 

This illustration shows two parallel lines crossing another pair of parallel lines. The segments of the parallel lines representing the train tracks on the road are 30 feet long.

 

The distance between the parallel rails is 4 ft 8.5 in. What is the area of the road between the tracks?

 

Compare your answers.