Question

In a triangle, area is numerically equal to its perimeter. Find area of it’s incircle.

Answer 1

The relation between area of a triangle A, its perimeter P and its inradius r is,

$\longrightarrow A=\dfrac{1}{2}Pr$

Given that area is numerically equal to its perimeter.

$\longrightarrow A=P$

$\longrightarrow P=\dfrac{1}{2}Pr$

Since perimeter is non - zero,

$\longrightarrow\dfrac{r}{2}=1$

$\longrightarrow r=2$

Hence the area of the incircle is,

$\longrightarrow A_r=\pi r^2$

$\longrightarrow\underline{\underline{A_r=4\pi}}$