Consider a parallelogram ABCD,

The diagonal AC divides it into two congruent triangles, ABC and ADC.

Area of ABCD = Area of ABC + Area of ADC

= 2 x Area of ABC (since the two triangles are congruent)

Or, Area of Parallelogram = Base (BC) x Height (AL)

Another side can be chosen as base.

Here, it can be shown that the area of ABCD = AB (base) x CL (height)

The height is the distance between the parallel sides depending upon the choice of base. If we denote the choice of side for base as b and the distance between the parallel sides as h, then

Area of Parallelogram = b x h

Illustration: Find the area of a parallelogram with a base of 25 cm and a height of 16.8 cm.

Solution

Area = b x h

Or, Area = 25 cm x 16.8 cm

= 420 cm²

Exercise: The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides.

Answer: 23.2 cm, Hint: 32 cm x 17.4 cm = 24 cm x h