What is the area of a regular pentagon with a side of 12 in.? Round the answer to the nearest tenth.
495.5 in.2
495.5 in. 2
311.8 in.2
311.8 in. 2
247.7 in.2
247.7 in. 2
124.7 in.2
The area of a regular pentagon can be calculated using the formula:
Area = (0.25 * n * s^2) / tan(180/n)
Where n is the number of sides (5 for a pentagon) and s is the length of each side (12 in.). Plugging in the values:
Area = (0.25 * 5 * 12^2) / tan(180/5)
Area = (0.25 * 5 * 144) / tan(36)
Area = 18 * 144 / 0.7265
Area = 2592 / 0.7265
Area ≈ 3568.093 in^2
Rounded to the nearest tenth, the area of the regular pentagon is 3568.1 in^2. This is not one of the available answer choices, so it seems that there may be a mistake in the provided options.