Answer:
- octagon: 483 ft²
- square: 400 ft²
Step-by-step explanation:
You want the areas of an octagon and a square, each with a perimeter of 80 ft.
Square
The side length of a square is 1/4 of its perimeter, so the square of interest has a side length of ...
(80 ft)/4 = 20 ft
The area is the square of the side length, so the area of the square is ...
A = s²
A = (20 ft)² = 400 ft²
Octagon
A regular octagon has 8 sides of equal length, so the side length is ...
(80 ft)/8 = 10 ft
The area is found by the formula ...
A = 2(1 +√2)s²
A = 2(1 +√2)(10 ft)² ≈ 483 ft²
The area of the octagon is about 483 square feet; about 400 square feet for the square.
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