Answer:
10.39 ft²
Explanation:
To answer the question, we need to know the following;
- A regular polygon is a polygon whose sides are equal
- A hexagon is a six sided polygon
- A regular hexagon is a polygon with six equal sides
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