The length of the adjacent side of a parallelogram are 37 and 51 cm respectively and the length of one it’s of its diagonal is 20 cm find the area of the parallelogram

Dear Vivek
 
Let the two adjacent sides of the parallelogram be a = 51 cm, b = 37 cm
Let the length of diagonal be c = 20 cm
These two sides and the diagonal forms a triangle
semi perimeter, s = (a + b + c) / 2
s = (51 + 37 + 20)/2 = 54 cm
By Heron's formula, we have area of triangle, Δ = √s(s - a)(s - b)(s - c)
= √[54(54 - 51)(54 - 37)(54 - 20)
= √54 x 3 x 17 x 34
= 306 sq cm
Area of parallelogram = 2 x area of triangle = 2 x 306 = 612 sq cm

Regards
Arun (askIITians forum expert)