Question

Find the area of a triangle whose sides are 42 cm, 34 cm and 20 cm.

Answer 1

To find the area of the triangle, we will first find the semiperimeter of the triangle.

Thus, we have:

$s=\frac{1}{2}\left(a+b+c\right)=\frac{1}{2}\left(42+34+20\right)=\frac{1}{2}\times 96=48\mathrm{cm}$

Now,

$$\begin{gathered} \mathrm{Area}ofthetriangle=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{48\left(48-42\right)\left(48-34\right)\left(48-20\right)} \\ =\sqrt{48\times 6\times 14\times 28} \\ =\sqrt{112896} \\ =336{\mathrm{cm}}^2 \end{gathered}$$