Question

What is the inradius of a regular hexagon of sides 6 cm?

• A. $2\sqrt{3}cm$
• B. $3\sqrt{3}cm$
• C. $3\sqrt{2}cm$
• D. 6 cm

Answer 1

The correct option is B

$3\sqrt{3}cm$

In a regular hexagon, two adjacent circumradii and the included side forms an equilateral triangle.

$\therefore$ The circumradius R of a regular hexagon = length of any side = 6 cm.

Now, we can find out the inradius r , using the Pythagoras theorem.

$R^2=r^2+3^2$

$\Rightarrow 6^2=r^2+3^2$

$\Rightarrow r^2=36-9=27$

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