Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are$26cm,28cmand30cm$, and the parallelogram stands on the base$28cm$, find the height of the parallelogram.

Answer 1

Step 1: Find the area of the triangle.

Using Heron’s formula, the area of the triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

So, the perimeter $=26+28+30=84cm$.

And it's semi-perimeter$=s=84/2cm=42cm$.

$$\begin{gathered} =\surd \left[42\right(42-26\left)\right(42-28\left)\right(42-30\left)\right]c{m}^2 \\ =\surd [42\times 16\times 14\times 12]c{m}^2 \\ =336c{m}^2 \end{gathered}$$

Step 2: calculate the height of the parallelogram.

Let the height of the parallelogram be$h$.

$Astheareaofparalle\log ram=areaofthetriangle,$

$$\begin{gathered} 28cm\times h=336c{m}^2 \\ h=\frac{336}{28}=12cm \end{gathered}$$

Hence, the height of the parallelogram is$12cm.$