Question

Find the radius of the incircle of a regular hexagon of side $24cm$

Answer 1

Using formula,

In circle radius $=\frac{a}{2\tan \frac{\pi }{n}}$

Where, $a=$ side of polygon

$\Rightarrow$ $n=$ number of sides

$\therefore$ For hexagon, $n=6$

Now, $r=\frac{24}{2\tan \left(\frac{180°}{6}\right)}=\frac{12}{\tan 30°}=\frac{12}{\frac{1}{\sqrt{3}}}$

$\Rightarrow r=12\sqrt{3}cm.$

Hence, the answer is $12\sqrt{3}cm.$