A regular hexagon has a radius of 20in. What is the approximate area of the hexagon

A = 1038 in² ...

Step-by-step explanation:

There are several ways to find the area of a regular hexagon

In a regular hexagon, split the figure into triangles.

Find the area of one triangle.

Multiply this value by six.

We will apply the formula of area of regular polygon:

A = 1/2r²nsin (360/n)

r = radius

n = number of sides of the regular polygon

We know that,

r = 20 in

n = 6

Now substitute the values in the formula:

A = 1/2 (20) ² (6) sin (360/6)

A = (20) ² (3) sin (360/6)

A = (20) ² (3) sin (60)

A=3 * (20) ² * √3/2

A = 1200 * √3/2

A = 600*√3

A = 1038 in² ...

Therefore the approximate area of hexagon is 1038 in² ...

A = 1038 in²