Question

Find area of triangle having three sides as $5cm,6cm$ and $7cm$

Answer 1

Solve for area of the required triangle

Given sides of triangle $a,b,c=5cm,6cm,7cm$ respectively.

According to Heron's formula,

Area of triangle$\mathbf{=}\sqrt{\mathbf{s}\left(s-a\right)\left(s-b\right)\left(s-c\right)}$, where $\mathit{s}\mathbf{=}\frac{\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{+}\mathbf{c}}{\mathbf{2}}$

Here, $s=\frac{5+6+7}{2}=9cm$

$\therefore$Area of triangle$=\sqrt{9\left(9-5\right)\left(9-6\right)\left(9-7\right)}$

$=\sqrt{9\times 4\times 3\times 2}=6\sqrt{6}c{m}^2$

Hence, area of the given triangle is $6\sqrt{6}c{m}^2$