The floor of the gazebo shown is a regular octagon. Each side of the floor is 8 feet, and the area is about 309 square feet. You build a small model gazebo in the shape of a regular octagon. The perimeter of the floor of the model gazebo is 7 feet. Find the area of the floor of the model gazebo to the nearest hundredth of a square foot. What is the ratio of the perimeters (in feet) of the real gazebo floor to the model gazebo floor?

Question

Mathematics

Kiara Hart

12 February, 18:51

The floor of the gazebo shown is a regular octagon. Each side of the floor is 8 feet, and the area is about 309 square feet. You build a small model gazebo in the shape of a regular octagon. The perimeter of the floor of the model gazebo is 7 feet. Find the area of the floor of the model gazebo to the nearest hundredth of a square foot. What is the ratio of the perimeters (in feet) of the real gazebo floor to the model gazebo floor?

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Answers (1)

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Ty Dunlap · Answer 1

Area: 3.7 ft²

Ratio: 73.14 : 1

Step-by-step explanation:

Perimeter of an octagon = 8*side

Replacing with perimeter = 7 ft:

7 = 8*side

side = 7/8 ft = 0.875 ft

that is, each side of the model is 7/8 ft length.

Area of an octagon = 2 * (1 + √2) * side²

Area of an octagon = 2 * (1 + √2) * (7/8) ²

Area of an octagon = 3.7 ft²

Perimeter of real gazebo = 8*8 = 64 ft

Then, the ratio of the perimeters (in feet) of the real gazebo floor to the model gazebo floor is 64:0.875. Multiplying each term by 8/7, we get 73.14:1