To show that the area of a trapezium is equal to half the product of its altitude and sum of its parallel sides.
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.
b1= 5 cm
b2= 11 cm
h= 8 cm
Area of trapezium = 1/2(b1+b2) X h
=1/2(11+5) X 8