The perimeter of a heptagon is the total length of the contour around the heptagon. This means that we can calculate the perimeter of heptagons by adding the lengths of the seven sides. In the case of regular heptagons, all seven sides have the same length, so we can obtain a simplified perimeter formula.
Here, we will learn about the formula used to calculate the perimeter of regular heptagons. In addition, we will look at some solved exercises in which we will apply this formula.
What is the formula to find the perimeter of a heptagon?
The perimeter of any figure is calculated by adding the lengths of all the sides. In the case of a heptagon, we have to add the lengths of the seven sides, so we have the following formula:
$latex p=a+b+c+d+e+f+g$
where, $latex a, ~b, ~c, ~d, ~e, ~f, ~g$ are the lengths of the sides of the heptagon.
If we have a regular heptagon, we know that the seven lengths are equal, so the formula becomes:
| $latex p=7a$ |
where a is the length of one of the sides of the heptagon.
Perimeter of a heptagon – Examples with answers
With the following examples, you can practice solving problems related to the perimeter of heptagons. Each example has its respective solution, but it is recommended that you try to solve the exercises yourself before looking at the answer.
EXAMPLE 1
What is the perimeter of a heptagon that has sides of length 6 m?
Solution
We can use the perimeter formula with $latex a=6$. Therefore, we have:
$latex p=7a$
$latex p=7(6)$
$latex p=42$
The perimeter of the heptagon is 42 m.
EXAMPLE 2
A heptagon has sides of length 11 m. What is its perimeter?
Solution
We have to use the perimeter formula with $latex a=11$. Therefore, we have:
$latex p=7a$
$latex p=7(11)$
$latex p=77$
The perimeter of the heptagon is 77 m.
EXAMPLE 3
What is the perimeter of a heptagon that has sides of length 23 m?
Solution
We use the length $latex a=23$ in the perimeter formula. Therefore, we have:
$latex p=7a$
$latex p=7(23)$
$latex p=161$
The perimeter of the heptagon is 161 m.
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EXAMPLE 4
A heptagon has a perimeter of 49 m. What is the length of its sides?
Solution
In this case, we start with the perimeter and want to find the length of one of the sides. We use the perimeter formula with $latex p=49$ and solve for a:
$latex p=7a$
$latex 49=7a$
$latex a=7$
The length of one of the sides is 7 m.
EXAMPLE 5
What is the length of the sides of a heptagon that has a perimeter of 147 m?
Solution
Similar to the previous problem, we use the perimeter formula with $latex p=147$ and solve for a:
$latex p=7a$
$latex 147=7a$
$latex a=21$
The length of the sides of the heptagon is 21 m.
Perimeter of a heptagon – Practice problems
Practice using the formula for the perimeter of heptagons to solve the following problems. If you need help with this, you can look at the solved examples above.
See also
Interested in learning more about parallelograms? Take a look at these pages:
