Measurement: Finding the Area of a Triangle

1. Deriving the formula to calculate area of a triangle.

In the figure below,
Area of the rectangle ABCD  =  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.

finding the area of a triangle
     Area of right-angled triangle
1
2
area of rectangle
1
2
 ×  (length  ×  width)
1
2
 ×  (base  ×  height)
Study the following examples.

formula to calculate the area of a triangle

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

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

finding the area of a triangle
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

3. Find the area of the shaded pentagon below.

finding the area of a triangle
     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