Question

find the area of parallelogram whose adjacent sides are 14 cm and 12 cm and the diagonal connected the ends is 18 .

use of H eron' s formula

Answer 1

First find area of triangle ABC , after thet 2×area of ∆ABC=area of \\gm

Answer 2

Perimeter of one triangle formed = 14 + 12 + 18 = 44

2s = 44cm

s = 22cm

Area of Triangle = √s(s-a)(s-b)(s-c) where a,b and c are the sides of the triangle.

= √22(22-12)(22-14)(22-18)

=√22 x 10 x 8 x 4

=√2 x 11 x 2 x 5 x 2 x 4 x 4

=2 x 4 √110 = 8√110 cm²

Therefore area of parallelogram = 2 x Area of Triangle

= 2 x 8√110

= 16√110 cm²

≈ 167.80 cm²