What is the area of a regular pentagon with a side length of 9.4 feet and an apothem length of 6.5 feet?
the pentagon consists of 5 triangles, each with altitude 6.5 and base 9.4
Now it's easy, right?
To find the area of a regular pentagon, you can use the formula:
Area = (Perimeter * Apothem) / 2
In this case, you are given the side length and the apothem length.
Step 1: Calculate the perimeter of the regular pentagon.
The perimeter of a regular pentagon is given by the formula:
Perimeter = 5 * Side Length
Given a side length of 9.4 feet, we can calculate the perimeter as:
Perimeter = 5 * 9.4 = 47 feet
Step 2: Substitute the calculated perimeter and the given apothem into the area formula.
Area = (Perimeter * Apothem) / 2
Area = (47 * 6.5) / 2
Step 3: Calculate the area.
Area = (47 * 6.5) / 2
Area = 305.5 / 2
Area = 152.75 square feet
Therefore, the area of the regular pentagon with a side length of 9.4 feet and an apothem length of 6.5 feet is 152.75 square feet.