Area of a Trapezium

In the adjoining figure, the side AB (a) and CD (b) of trapezium ABCD are parallel to each other. AE = BG = h is the height of the trapezium and AC is the diagonal.

Now,

Area of trapezium (A) = Area of ΔADC + Area of ΔABC

= ½ CD × AE + ½ AB × BG

= ½ b × h + ½ a × h

= ½ h × (a + b)

Hence,

Area of trapezium = ½ h × (a + b)

= ½ height × sum of parallel sides