Question

A regular hexagon is inscribed inside of a circle with a radius of 6 cm. Find the area of the shaded region inside the circle.

Answer 1

19.6

Explanation:

Area of circle - Area of Hexagon

pi 6^2 - 3sqrt3/2 *6^2

Answer 2

Based on the given information, the area of the shaded region is approximately 19.6
`cm^2`. Option 3

How to calculate area of shaded region

Given:

Radius of the circle = 6 cm

To find the shaded area (outside the regular hexagon but inside the circle), find the area of the circle and subtract the area of the regular hexagon.

Area of the Circle:

The formula for the area of a circle is

π
`r^2`.

So, the area of the circle with a radius of 6 cm is

π ×
`6^2`

=36π
`cm^2`.

Area of the Regular Hexagon:

The hexagon is inscribed in the circle, and its side length is equal to the radius of the circle.

The formula for the area of a regular hexagon is

`(3 \sqrt3)/2 * side^2`

For the side length of 6 cm, the area of the regular hexagon is

`(3 \sqrt3)/2 * 6^2 \\\\= 54 \sqrt3`
`cm^2`.

Now, to find the shaded area, subtract the area of the hexagon from the area of the circle:

Shaded area = Area of circle - Area of hexagon

Shaded area = 36π−54
`\sqrt3`

​

Approximating the values:

Shaded area ≈ 113.1−93.53=19.57
`cm^2`

Rounded to one decimal place, the area of the shaded region is approximately 19.6
`cm^2`.