Question

If two adjacent sides of a parallelogram are 11cm and 15 cm and one of its diagonals is 16 cm, then find the area of the parallelogram

Answer 1

Let the two adjacent sides of the parallelogram be a = 11 cm, b = 15cm
Let the length of diagonal be c = 16 cm
These two sides and the diagonal forms a triangle
semi perimeter, s = (a + b + c) / 2
s = (11 + 15 + 16)/2 = 21 cm
By Heron's formula, we have area of triangle, Δ = √s(s - a)(s - b)(s - c)
= √[21(21-11)(21-15)(21-16)
= √21*10*6*5
= 60√7sq cm
Area of parallelogram = 2 x area of triangle = 2 x 60√7= 120√7cm