Area of trapezium

To show that the area of a trapezium is equal to half the product of its altitude and sum of its parallel sides.

- Trapezium is a quadrilateral with one pair of opposite sides parallel.
- A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and equal to each other.
- The parallel sides are called "bases" of the trapezium and the other two sides are called the "legs" of trapezium.
- Area of parallelogram = base(b) X height(h)

Consider trapezium ABCD. AB and DC are the bases (parallel sides) and h is the height of trapezium ABCD.

A parallelogram can be formed by creating a copy of trapezium ABCD and placing it inverted touching side BC as shown in figure below:

We observe that parallelogram ASPD is formed by combining two trapeziums ABCD and BSPC.

∴ Area of trapezium ABCD = 1/2 X Area of parallelogram ASPD

= ½ X DP X h

= 1/2 X (DC+CP) X h

=1/2 X (b1 + b2) X h

= ½ X (AB + DC) X h

Thus, area of a trapezium is equal to half the product of its altitude and sum of its parallel sides.

Find the area of the following trapezium.

Given,

b1= 5 cm

b2= 11 cm

h= 8 cm

Area of trapezium = 1/2(b1+b2) X h

=1/2(11+5) X 8

=64 cm²