Aregular hexagon has sides of 2 feet. what is the area of the hexagon? 12 ft2 12 ft2 24 ft2 6 ft2

10.39 ft²

Step-by-step explanation:

To answer the question, we need to know the following;

In this case, the length of one side of the hexagon is 2ft

We are required to determine the area of the hexagon;

We need to determine the number of triangles we can divide an hexagon into triangles from its center, then determine the center angle of each triangle.

Center angle = 360° ÷ 6

                      = 60°

Therefore, we have six isosceles triangles whose base side is 2 ft in length and the one angle at the top is 60°

Dividing the a triangle into two we have two right angled triangle each with an angle of 30° and one of the shorter side as 1 ft.

Using trigonometric ratios we can determine the other side.

tan 30 = opp/adj. opposite is 1 side

Adj = 1 ft ÷ tan 30

      = 1.732 ft

Therefore, the area of each triangle = 0.5 × 1 ft × 1.732 ft × 2

                                                            = 1.732 ft²

Therefore, the area of a hexagon = 6 × 0.5 × 1 ft × 1.732 ft

                                                        = 10.392 ft²

Thus, the area of the hexagon is 10.39 ft²