The gazebo in the photo is built in the shape of a regular octagon. Each side is 13ft long and the enclosed area is 816.4ft^2What is the length of the apothem?

slaggingV 2020-12-16 Answered

The gazebo in the photo is built in the shape of a regular octagon. Each side is 13ft long and the enclosed area is \(816.4ft^2\)
What is the length of the apothem?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Gennenzip
Answered 2020-12-17 Author has 22238 answers

Use the formula for the area of a regular polygon with nn sides with length ss and apothem a:
\(\displaystyle{A}=\frac{{1}}{{2}}{a}{n}{s}\)
Substitute \(A=816.4 ft^2\), n=8, and s=13 ft: \(\displaystyle{816.4}=\frac{{1}}{{2}}{\left({a}\right)}{\left({8}\right)}{\left({13}\right)}\)
816.4=52a
15.7=a
So, the length of the apothem is 15.7 ft.

Not exactly what you’re looking for?
Ask My Question
37
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-06
The gazebo in the photo is built in the shape of a regular octagon. Each side is 6 ft long, and the enclosed area is 172.8 ft². What is the length of the apothem?
asked 2021-05-14
The volume of a can (right circular cylinder) is 10 cubic feet. The curved surface area is the area of the side. Write the curved surface area S as a function of the radius r. Write the radius r as a function of the curved surface area S.
asked 2021-05-09
A wire of length r feet is bent into a rectangle whose width is 2 times its height. Write the area A of the rectangle as a function of the wire's length r. Write the wire's length r as a function of the area A of the rectangle (note A not a).
asked 2020-12-15

The area of a rectangular cloth is \((6x^2 - 19x - 85)\) cm2. The length is (2x + 5) cm. Find the width.

asked 2020-11-27

A regular hexagon is dilated by a scale factor of \(\frac{4}{3}\) to create a new hexagon. How does the perimeter of the new hexagon compare with the original perimeter?

asked 2021-05-19

The volume of a cube is increasing at the rate of \(1200\ cm\ \frac{sup}{min}\) at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

asked 2021-05-30
A certain television is advertised as a 50 -inch TV(the diagonal length). If the width of the TVis 14 inches, how many inches tall is the TV?
...