Final answer:
To find the area of a regular pentagon, you can multiply half the perimeter by the apothem. In this case, with a side length of 5.8ft and an apothem of 4.0ft, the area is computed as 58 square feet.
Step-by-step explanation:
To calculate the area of a regular pentagon, you can use the formula for the area of a polygon which is:
Area = ½ × Perimeter × Apothem.
Given a regular pentagon with a side length of approximately 5.8 feet and an apothem of approximately 4.0 feet, first find the perimeter by multiplying the side length by the number of sides, which is 5 in this case. So, the perimeter (P) is 5.8 ft × 5 = 29 ft.
Then apply the formula to find the area (A):
A = ½ × P × Apothem
A = ½ × 29 ft × 4.0 ft
A = 58 ft².
Therefore, the area of the pentagon is 58 square feet.