Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 11 cm, 15 cm and 6 cm, and the parallelogram stands on the base 15 cm, find the height of the parallelogram.[4 Marks]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Area of the triangle using hero’s formula,

S = $\frac{Perimeter}{2}$ = $\frac{(11+15+6)}{2}$ =16 cm

Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
=$\sqrt{16(16-11)(16-15)(16-6)}$
= 20$\sqrt{2}$ $c{m}^2$

Now area of parallelogram = area of triangle
i.e., base × height = 20$\sqrt{2}$

As base =15cm $\Rightarrow$ Height = $\frac{20\sqrt{2}}{15}$=1.88cm