Question

Find the area of the triangle if its sides are $21cm,17cm,10cm.$

Answer 1

Step 1: Finding the semi perimeter of the triangle

Given sides of the triangle are $21cm,17cm,10cm.$

Since the triangle is a scalene triangle,

Area of the scalene triangle $=$ $\sqrt{s(s-a)(s-b)(s-c)}$, where $a,b,c$ are sides of the triangle and $s$ is the semi-perimeter.

$s=\frac{a+b+c}{2}$

$$\begin{gathered} s=\frac{21+17+10}{2} \\ =\frac{48}{2} \\ =24cm \end{gathered}$$

Step 2: Finding the area of the triangle

$$\begin{gathered} s-a=24-21=3cm \\ s-b=24-17=7cm \\ s-c=24-10=14cm \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{24\times 3\times 7\times 14} \\ =\sqrt{8\times 3\times 3\times 7\times 7\times 2} \\ =7\times 3\times 2\times 2 \\ =84c{m}^2 \end{gathered}$$

Hence. the area of the triangle is $84c{m}^2.$