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Answer :
Final answer:
The area of a regular pentagon with a side length of 4 feet and an apothem of 2 feet is found using the formula A = 1/2 × perimeter × apothem, giving an area of 37.2 ft² when rounded to the nearest tenth.
Explanation:
The question asks for the area of a cover for a hot tub in the shape of a regular pentagon with a given side length of 4 feet and an apothem of approximately 2 feet.
The area of the pentagon can be calculated using the formula A = ½ × perimeter × apothem, where the perimeter is the sum of the lengths of all sides of the pentagon.
Given that the pentagon is regular, it has equal sides, so the perimeter is 5 × 4 feet, which is 20 feet. Now, substitute the known values into the area formula: A = ½ × 20 ft × 2 ft = 20 ft².
Therefore, the correct answer is B - 37.2 ft², which is obtained by rounding the calculated area to the nearest tenth.
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