What is the area of the regular polygon?

Step-by-step explanation:

The area of a regular polygon is given by

where is the apothem and is the perimeter of the triangle.

The interior angle of a regular hexagon is

The line from the center to the given vertex bisects the 120 degree angle.

The hexagon is therefore divided into 6 equilateral triangles.

The apothem can be found using

This implies that;

Recall that an equilateral triangle has all sides equal hence the perimeter of the regular hexagon is

The area of the regular hexagon now becomes;

This simplifies to;

answer is c chief it always is