Can you help me with this?
Find the area of each regular polygon. Round to the nearest tenth.
1. an equilateral triangle with an apothem 8.9 inches long
Sure! To find the area of a regular polygon, you need to know the length of the apothem (the distance from the center of the polygon to the midpoint of any side) and the number of sides.
In the case of an equilateral triangle, all sides are equal, so the length of one side is also 8.9 inches. The formula for finding the area of an equilateral triangle is:
Area = (s^2 * √3) / 4
where "s" represents the length of one side.
Let's substitute the given value into the formula:
Area = (8.9^2 * √3) / 4
Calculating this expression, we get:
Area = (79.21 * 1.732) / 4
Area ≈ 136.629 / 4
Area ≈ 34.15725
Rounding to the nearest tenth, the area of the equilateral triangle is approximately 34.2 square inches.