A regular hexagon is inscribed in a circle. If the radius of the circle is 16 cm, what is the closest area of the hexagon.

178 cm^2

153.1 cm^2

665.1 cm^2

443.4 cm^2

Try / /

Step-by-step explanation:

176.1

units

2

Explanation:

A

shaded

=

A

circle

-

A

hexagon

A

circle

=

π

r

2

=

π

⋅

18

2

=

324

π

We can split up the hexagon into 6 regular triangles.

A

hexagon

=

6

⋅

A

triangle

=

6

⋅

1

2

b

h

Since the triangles are regular, the base is equal to the radius,

18

. We can represent the height by taking one of the triangles and drawing a line down the middle. The newly formed triangle is a

30

°

-

60

°

-

90

°

right triangle.