Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.

Answer 1

It is given that the area of triangle and parallelogram are equal.

We will calculate the area of triangle with the given values and it will also give us the area of parallelogram as both are equal.

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

, where

Therefore the area of a triangle; say A, having sides 15 cm, 13 cm and 14 cm is given by

a = 15 cm ; b = 13 cm ; c = 14 cm

We have to find the height of the parallelogram, say h

Area of parallelogram AECD say A₁ is given by

Base = 60 cm; Height = h cm; A =A₁ = 84 cm²