Question

If the lengths of the sides of a triangular plot of land are 20 m, 21 m and 13 m, what is its area?

Answer 1

Lengths of the sides of the triangle are 20 m, 21 m and 13 m.
Semi-perimeter of a triangle = $s=\frac{a+b+c}{2}$
Semi-perimeter = $=\frac{20+21+13}{2}=27\mathrm{m}$
Area of a triangle$=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$$\begin{gathered} =\sqrt{27\left(27-20\right)\left(27-21\right)\left(27-13\right)} \\ =\sqrt{27\left(7\right)\left(6\right)\left(14\right)} \\ =\sqrt{15876} \\ =126 \end{gathered}$$
∴ Area of the triangle is 126 sq m.