Question

Find the area of the triangle whose sides are $42cm,39cm,45cm$

Answer 1

Step 1:Finding the semi perimeter of the triangle :

Given sides of the triangle are $42cm,39cm,45cm$

Since the triangle is a scalene triangle,

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

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

$$\begin{gathered} s=\frac{42+39+45}{2} \\ =\frac{126}{2} \\ =63cm. \end{gathered}$$

Step 2 Finding the area of the triangle:

$$\begin{gathered} s-a=63-42=21cm \\ s-b=63-39=24cm \\ s-c=63-45=18cm \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{63\times 21\times 24\times 18} \\ =\sqrt{9\times 7\times 7\times 3\times 8\times 3\times 9\times 2} \\ =9\times 4\times 7\times 3 \\ =756c{m}^2. \end{gathered}$$

Hence the area of the triangle is $756c{m}^2.$