Question

Find the area of the triangle whose sides are $52cm,60cm,56cm$

Answer 1

Step 1: Finding the semi perimeter of the triangle

Given sides of the triangle are $52cm,60cm,56cm$

Since the triangle is a scalene triangle,

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

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

$\begin{array}{rcl}s& =& \frac{56+60+56}{2}\\ s& =& \frac{168}{2}\\ s& =& 84cm\end{array}$

Step 2: Finding the area of the triangle

$\begin{array}{rcl}s-a& =& 84-21=32cm\\ s-b& =& 84-17=24cm\\ s-c& =& 84-10=28cm\\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}& =& \sqrt{s(s-a)(s-b)(s-c)}\\ & =& \sqrt{84\times 32\times 24\times 28}\\ & =& \sqrt{12\times 7\times 8\times 3\times 12\times 2\times 7\times 4}\\ & =& 8\times 4\times 7\times 6\\ & =& 1344c{m}^2.\end{array}$

Hence, the area of the triangle is $1344c{m}^2.$