Question

Find the area of the regular hexagon if a side is 20 cm. Round to the nearest whole number.

A.) 886 cm^2
B.) 1673 cm^2
C.) 1039 cm^2
D.) 2079 cm^2

Answer 1

1039 cm^2.

Explanation:

The internal angle of a regular hexagon = 120 degrees.

A regular hexagon can be broken up into 6 isosceles triangles with base 20 cm. The base angle of one of these triangle = 1/2 * 120 = 60 degrees.

So the height of a triangle is calculated from the equation tan 60 = h / 10 so h = 10 tan 60

and the area of a triangle = 1/2 base * height

= 1/2 * 20 * 10 tan60

= 173.205 cm^2

making the area of the hexagon

= 6 * 173.205

= 1039 cm^2.

Answer 2

Area
= { (3✓3)/2 } *20^2
= (3*1.732/2)*400
=(1.5*1.732)*400
=1039.2

So the answer will be option (C)