Question

If the sides of a triangle are 25 cm, 39 cm and 56 cm, what is its area?

Answer 1

Lengths of the sides of the triangle are 25 cm, 56 cm and 39 cm.
Semi-perimeter of a triangle = $s=\frac{a+b+c}{2}$
Semi-perimeter = $\frac{25+39+56}{2}=60\mathrm{cm}$
Area of a triangle = $=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$
$$\begin{gathered} =\sqrt{60\left(60-56\right)\left(60-39\right)\left(60-25\right)} \\ =\sqrt{60\left(4\right)\left(21\right)\left(35\right)} \\ =\sqrt{176400} \\ =420 \end{gathered}$$
∴ Area of the triangle is 420 sq cm.