Question

Two adjacent side of a parallelogram are 74cm and 40cm and it's diagonal 102cm. Find its area.

Answer 1

Let the two adjacent sides of the parallelogram be a = 74 cm, b = 40 cm

Let the length of diagonal be c = 102 cm

These two sides and the diagonal forms a triangle

semi perimeter, s = (a + b + c)/2

s = (74 + 40 + 102)/2 = 216/2 = 108 cm

By Heron formula, we have area of triangle, Δ = √[s(s - a)(s - b)(s - c)]

. = √[108(108 - 4)(108 - 40)(108 - 102)]

= √{108 * 34 * 68 * 6}

= √{3 * 4 * 9 * 34 * 2 * 34 * 6}

= √{3 * 4 * 9 * 34 * 2 * 34 * 6}

= √{6 * 4 * 9 * 34 * 34 * 6}

= 6 * 2 * 3 * 34

= 1224 sq cm

Area of parallelogram = 2 * area of triangle = 2 * 1224 = 2448 sq cm