Measurement: Finding the Area of a Triangle

What is the formula to calculate the area of a triangle?

Take the rectangle ABCD below.
The area of the rectangle = length × width

Cut the rectangle into 2.
Now, each half is a right-angled triangle.
And, each right-angled triangle, therefore, has half the area of the rectangle.

 Area of right-angled triangle = 12 of area of rectangle = 12 × length × width) = 12 × base × height

Study the following examples.

In both examples above, the area of the triangle is half the area of the rectangle made by the base and height.

 So, Area of a triangle = 12 of area of rectangle made by the base and height = 12 × base × height

 The area of a triangle  = 12 × base × height

Read also: Identifying the base and height of a triangle

Calculating the area of triangles using formula

Example 1:

Find the area of a triangle that has a base of 3 cm and a height of 6 cm.

Both triangles above have a base of 3 cm and a height of 6 cm. Therefore, they both have the same area which is calculated as below:

 Area of triangle = 12 × base × height = 12 × 3 cm × 6 cm = 9 cm2

Example 2:

Find the area of the shaded pentagon below.

 Area of triangle ABC = 12 × (1.5 cm + 2 cm + 1.5 cm) × 4 cm = 12 × 5 cm × 4 cm = 10 cm2

 Area of triangle BED = 12 × 1.5 cm × 1 cm = 0.75 cm2

 Area of triangle GFC = 12 × 1.5 cm × 3 cm = 2.25 cm2

 Area of pentagon ADEFG =  Area (ABC) − Area (BED) − Area (GFC) =  10 cm2 − 0.75 cm2 − 2.25 cm2 =  7 cm2