The perimeter of a geometric figure is the total length around its outline. This length can be calculated by adding the lengths of all the sides of the figure. In the case of octagons, we can calculate their perimeter by adding the eight lengths of their sides. If we have a regular octagon, we simply need the length of one side to calculate the perimeter.
Here, we will learn about the formula that we can use to calculate the perimeter of octagons. In addition, we will look at some problems in which we will apply this formula to obtain the result.
What is the formula to find the perimeter of an octagon?
We can calculate the perimeter of a polygon by adding the lengths of all its sides. In the case of an octagon, we have to add the lengths of the eight sides, so we have:
$latex p=a+b+c+d+e+f+g+h$
where $latex a, ~b, ~c, ~d, ~e, ~f, ~g, ~h$ are the eight lengths of the sides of the hexagon.
If the octagon is regular, we know that the lengths of all its sides are equal, so we only need to use the length of one side. Therefore, the perimeter of a regular octagon is:
| $latex p=8a$ |
where a is the length of one of the sides of the regular octagon.
Perimeter of an octagon – Examples with answers
The following exercises can be used to practice using the formula for the perimeter of octagons. Try to solve the problems yourself before looking at the answer.
EXAMPLE 1
An octagon has sides of length 5 m. What is its perimeter?
Solution
We use the perimeter formula with $latex a=5$. Therefore, we have:
$latex p=8a$
$latex p=8(5)$
$latex p=40$
The perimeter of the hexagon is 40 m.
EXAMPLE 2
An octagon has sides of length 8 m. What is its perimeter?
Solution
We plug the value $latex a=8$ into the formula for the perimeter of the octagon. Therefore, we have:
$latex p=8a$
$latex p=8(8)$
$latex p=64$
The perimeter of the octagon is 64 m.
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EXAMPLE 3
If an octagon has sides of length 15 m, what is its perimeter?
Solution
We have the length $latex a=15$. Using this value in the perimeter formula, we have:
$latex p=8a$
$latex p=8(15)$
$latex p=120$
The perimeter of the octagon is 120 m.
EXAMPLE 4
What is the length of the sides of an octagon that has a perimeter of 112 cm?
Solution
In this question, we have the value of the perimeter and we want to find the length of the sides of the octagon. Therefore, we use $latex p=112$ in the formula and solve for a:
$latex p=8a$
$latex 112=8a$
$latex a=14$
The length of the sides of the octagon is 14 cm.
EXAMPLE 5
An octagon has a perimeter of 152 m. What is the length of the sides?
Solution
We use the perimeter formula with $latex p=152$ and solve for a:
$latex p=8a$
$latex 152=8a$
$latex a=19$
The length of the sides is 19 m.
Perimeter of an octagon – Practice problems
Practice applying the formula for the perimeter of octagons with the following problems. Choose an answer and check that it is correct by clicking “Check.”
See also
Interested in learning more about octagons? Take a look at these pages:
