What is the area of a regular pentagon with a side of side of 12in? Round the answer to the nearest tenth.
495.5 in^2
311.8in^2
247.7in^2
124.7in^2
The formula for the area of a regular pentagon is (s^2 * sqrt(25 + 10 * sqrt(5))) / 4, where s is the length of one side.
Plugging in the given side length of 12in into the formula, we get:
Area = (12^2 * sqrt(25 + 10 * sqrt(5))) / 4
≈ (144 * sqrt(25 + 10 * sqrt(5))) / 4
≈ (144 * sqrt(25 + 10 * 2.236)) / 4
≈ (144 * sqrt(25 + 22.36)) / 4
≈ (144 * sqrt(47.36)) / 4
≈ (144 * 6.88191) / 4
≈ 966.5664 / 4
≈ 241.6416
Rounding this answer to the nearest tenth, the area of the regular pentagon is approximately 241.6in^2.
Therefore, the correct answer is:
241.6in^2