Question

ABCDEF is a regular hexagon of side $3cm$. At each corner is drawn a circle of radius $1cm$. The area of the shaded part is

• A. $1.57c{m}^2$
• B. $9.42c{m}^2$
• C. $6.28c{m}^2$
• D. $3.14c{m}^2$

Answer 1

The correct option is C $6.28c{m}^2$

Each angles $=\frac{180{(6-2)}^{\circ }}{6}={120}^{\circ }$

Area of 1 sector $=\frac{120}{360}\times 3.14\times 1^{2}c{m}^2$

$=\frac{3.14}{3}c{m}^2$

$\therefore$ Area of 6 sectors $=6\times \frac{3.14}{3}c{m}^2$
$=6.28c{m}^2$