Question

In figure, a regular hexagon of side length $5$ cm is inscribed in a circle. Calculate the percentage of the circle that is shaded, to the nearest tenth.

• A. $13.6$%
• B. $17.3$%
• C. $78.5$%
• D. $82.7$%
• E. $86.4$%

Answer 1

The correct option is B $17.3$%

Radius of circle is equal to side length of hexagon, which is equal to $5$
Area of circle is $\pi (5{)}^2=78.57$
Area of hexagon is $6\times \frac{1}{2}\times 5\times 5\times \sin 60=64.95$
Area of shaded region is $78.57-64.95=13.62$
Percentage is $\frac{13.62}{78.57}\times 100=17.3\%$