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  =  1
2
  of area of rectangle
   =  1
2
   × length × width)
   =  1
2
  × 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  =  1
2
  of area of rectangle made by the base and height
   =  1
2
  × base × height

The area of a triangle  =  1
2
  × 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  =  1
2
  × base × height
   =  1
2
  × 3 cm × 6 cm
   =  9 cm2


Example 2:

Find the area of the shaded pentagon below.



Area of triangle ABC  =  1
2
  × (1.5 cm + 2 cm + 1.5 cm) × 4 cm
   =  1
2
  × 5 cm × 4 cm
   =  10 cm2


Area of triangle BED  =  1
2
  × 1.5 cm × 1 cm
   =  0.75 cm2


Area of triangle GFC  =  1
2
  × 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