Question

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

Answer 1

Now in ∆ABC

AB = a = 34 cm, BC = b = 20 cm, AC = c = 42 cm 

Let a, b and c are the sides of triangle and s is 

the semi-perimeter, then its area is given by:

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)where s = \(\frac{a+b+c}2\)

s = \(\frac{a+b+c}2\) = \(\frac{34+20+42}2\) = 48

A = \(\sqrt{48(48-34)(48-20)(48-42)}\) cm²

a = \(\sqrt{48\times14\times28\times6}\) = 336 cm²

Hence, area of Parallelograme ABCD =2 × 336 =672 cm²