One side of a parallelogram is 10 cm and its diagonals are 16 cm and 24 cm respectively. Find its area

The parallelogram is made up of four triangles made up of the diagonals and four sides. The areas can be found using Heron's Formula. For a triangle with three sides, a, b, & c:

s = (a+b+c) / 2; Area = squareroot(s(s-a)(s-b)(s-c))

The point of intersection of the diagonals is at the midpoint of each diagonal, since diagonals of a parallelogram bisect each other. If the three sides of one triangle is a = 8, b = 12, c = 10

s = (8+12+10) = 15

A = sqrt(15(15-8)(15-12)(15-10)) = 39.66.

The areas of the four interior triangles of a parallelogram are equal, therefore

A(parallelogram) = 4(39.7) = 159