answersLogoWhite

0


Best Answer

Given: ABCDEFGH is a regular octagon; diameter (diagonal) = d

Let the side length of the octagon be s.

Label with O the intersection of the diagonals.

Look at the formed isosceles triangle AOB.

Draw the apothem OK, which is also the altitude of the triangle AOB, which bisect the side AB.

Look at the right triangle AOK. Here we have:

The length of AK is s/2.

The length of AO is d/2.

The angle A is 67.5° (135°/2)

So that,

cos 67.5° = (s/2)/(d/2)

.383 = s/d

(.383)d = (s/d)(d)

(.383)d = s

Thus, the side length of the octagon equals (.383)d.

User Avatar

Wiki User

14y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: How does one find the length of sides of an octagon given its diameter?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

What is the diameter of an octogon when each side is 18 inches in length?

An octagon is a polygon with 8 sides. To find the diameter of a regular octagon when each side is 18 inches in length, you can use the formula: Diameter = Side length × √(2 + √2) Plugging in the given side length (18 inches): Diameter = 18 × √(2 + √2) ≈ 56.97 inches So, the diameter of the octagon is approximately 56.97 inches.


How do you construct an octagon with a given side?

a regular octagon has the same length all sides. so with the given angle draw 8 sides at an angle of 135 degrees from each other


What is the diameter of an octagon if the sides are 11 feet?

The diameter of an octagon with sides of 11 feet can take any value between 0 feet and 44 feet.


What is the length of each side of an octagon that is 48 inches in diameter?

Since the diameter is 48 inches, and there are 8 sides, then each side will be 48/8 = 6 inches.


What are equals in an octagon?

Octagon just means it has 8 sides. Regular octagon means it has 8 sides of the same length and the angles are equal.


Are any of a octagons sides equal in length?

They can be. A regular octagon has all sides of equal length.


What is the diameter of an octagon with 24 inch sides?

I think the diameter is 58"


How does a not regular octagon look like?

An octagon has eight sides. A regular octagon is one that has eight sides of equal length, and all the angles are of the same measure. Anything else - sides that are not all the same length, or not all angles the same - would be a non-regular octagon.


What is a octagon that is not regular?

An irregular octagon has eight sides, but they aren't all of equal length


Can an octagon look different?

An octagon is any figure that has 8 sides, no one said that all of the sides had to be the same length.


What is the sum of measures of an octagon?

It depends how long each side is. An octagon's sides do not have to all be the same length, they can vary from octagon to octagon. A regular octagon's sides are all equal so the sum of their measures would be 8 times the length of any one side..


What is an octagon that is not irregular?

An octagon that is not irregular is a regular octagon, one in which each of the eight sides os the same length