What is the area of a regular 15-gon with a perimeter of 90 m? (1 point) Responses 528.2 m² 528.2 m² 635.1 m² 635.1 m² 1,270.3 m² 1,270.3 m² 142,903.1 m²

To find the area of a regular polygon, we can use the formula:

Area = 0.5 * perimeter * apothem

First, we need to find the apothem of the 15-gon. Since it is a regular polygon, we can divide it into 15 equal triangles. The central angle of each triangle is 360 degrees / 15 = 24 degrees. The apothem can be found by using trigonometry:

apothem = (side length / 2) * tan(24 degrees)
side length = perimeter / 15 = 90 m / 15 = 6 m

apothem = 3 * tan(24 degrees) ≈ 2.3 m

Now we can calculate the area:

Area = 0.5 * 90 m * 2.3 m = 103.5 m²

Therefore, the area of the regular 15-gon is approximately 103.5 m². Since it is not one of the multiple-choice options, there may have been a mistake in the assumptions or calculations.