Question

Maryann has a hexagonal deck that needs to be painted. The apothem's length is 7 ft, and one side is 8 ft. What is the square footage of her deck?

A. 168 sq. ft.
B. 100 sq. ft.
C. 56 sq. ft.
D. 112 sq. ft.

Answer 1

To find the square footage of Maryann's hexagonal deck, we use the area formula for a regular polygon. With a perimeter of 48 ft (6 sides of 8 ft each) and an apothem of 7 ft, we calculate the area to be 168 sq. ft.

Step-by-step explanation:

To determine the square footage of Maryann's hexagonal deck, we can use the formula for the area of a regular polygon which is Area = (1/2) × Perimeter × Apothem. Since we know the length of one side is 8 ft and the apothem is 7 ft, the perimeter (P) would be 8 ft multiplied by 6 (since a hexagon has 6 sides), giving us 48 ft. Plugging these values into the formula, we get the area as:

Area = (1/2) × P × Apothem
Area = (1/2) × 48 ft × 7 ft
Area = 24 ft × 7 ft
Area = 168 sq. ft.

Hence, the correct answer is A. 168 sq. ft.