Question

ABCDEF is a regular hexagon of side 12cm.Then find the following and match it.

• A. 12cm
• B. 24cm
• C. $6\sqrt{3}$ cm
• D. ${120}^{\circ }$

Answer 1

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

$\therefore$ The circumradius of a regular hexagon = length of any side = 12 cm

Diagonal AD = Diameter of circumcircle = 2$\times$12=24cm

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

$R^2=r^2+3^2$ where R is circumradius and r inradius

$\Rightarrow {12}^2=r^2+6^2$

$\Rightarrow r^2=144-36=108$

$\Rightarrow$ inradius r = $6\sqrt{3}cm$

the interior angle of a regular polygon of n sides = $\frac{(n-2)\times {180}^{\circ }}{n}$

$\therefore$ The interior angle of a regular octagon = $\frac{(6-2)\times {180}^{\circ }}{6}$ = $\frac{4\times {180}^{\circ }}{6}$ = ${120}^{\circ }$

$\therefore \angle BAC={120}^{\circ }$