find the area of the regular polygon. give the answer to the nearest tenth. a hexagon with a radius of 12.5ft
a. 259.8ft
b. 65.0ft
c. 129.9ft
d. 406.1ft
The formula to find the area of a regular polygon is A = 1/2 * apothem * perimeter.
In this case, the apothem of the hexagon with a radius of 12.5 ft can be found using trigonometry. The apothem is equal to the radius times the cosine of the central angle (60 degrees in this case).
Apothem = 12.5 ft * cos(60 degrees) = 6.25 ft * 0.5 = 3.125 ft
The perimeter of a hexagon can be found by multiplying the length of one side by 6.
Perimeter = 12.5 ft * 6 = 75 ft
Now, plug the values into the area formula:
A = 1/2 * 3.125 ft * 75 ft = 3.90625 ft * 75 ft ≈ 292.9 ft
Therefore, the area of the regular hexagon to the nearest tenth is 292.9 ft, closest to option:
a. 259.8ft.