Question

The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center of the octagon to one of the vertices is 11.8 feet. What is the approximate length of the apothem? feet What is the approximate area of the floor of the gazebo? square feet

Answer 1

The answer is:

a = 10.91 feet

b = 392.76 feet²

Hope it helps!

Answer 2

The length of one side of the octagon is given by:

`L = 72/8 L = 9`
Then, the apothem can be determined using the Pythagorean theorem in the following way:

`11.8 ^ 2 = (9/2) ^ 2 + a ^ 2`
Clearing to have:

`a ^ 2 = 11.8 ^ 2 - (9/2) ^ 2`

`a = √(11.8 ^ 2 - (9/2) ^ 2)`

`a = 10.91`
Then, the area is given by:

`A = (8) * (1/2) * (L) * (a)`
Where,
L: length of the octagon sides
a: apotema
Substituting values:

`A = (8) * (1/2) * (9) * (10.91) A = 392.76 feet ^ 2`
Answer:
the approximate length of the apothem is:
a = 10.91 feet
The approximate area of the floor of the gazebo is:
A = 392.76 feet ^ 2