Use the diagram of a regular polygon to find the area:

Question

3.44ft
5ft
Area=

Answer 1

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

Area = 1/2 * Perimeter * Apothem

First, we need to find the perimeter of the regular polygon. Since the polygon has 5 sides and each side is 3.44 ft, the perimeter will be:

Perimeter = 5 * 3.44ft = 17.2ft

Next, we need to find the apothem of the regular polygon. The apothem is the distance from the center of the polygon to the midpoint of any side. To find the apothem, we can use the formula:

Apothem = side length / (2 * tan(180 degrees / number of sides))

Apothem = 3.44ft / (2 * tan(180 degrees / 5))
Apothem = 3.44ft / (2 * tan(36 degrees))
Apothem = 3.44ft / (2 * 0.7265)
Apothem = 3.44ft / 1.453
Apothem = 2.37ft

Now, we can calculate the area of the regular polygon using the formula:

Area = 1/2 * Perimeter * Apothem
Area = 1/2 * 17.2ft * 2.37ft
Area = 9.86ft^2

Therefore, the area of the regular polygon is 9.86 square feet.