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147 LearnersLast updated on September 26, 2025
Perimeter of Heptagon
The perimeter of a shape is the total length of its boundary. The sum of all seven sides is called the perimeter of a heptagon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a heptagon.
What is the Perimeter of a Heptagon?
The perimeter of a heptagon is the total length of its seven sides. By adding the length of all seven sides, we get the perimeter of the shape.
The formula for the perimeter of a heptagon is π = π + π + π + π + π + π + π, where a, b, c, d, e, f, and g are the sides of the heptagon.
For instance, if a heptagon has sides a = 4, b = 5, c = 6, d = 7, e = 8, f = 9, and g = 10, then its perimeter is p = 4 + 5 + 6 + 7 + 8 + 9 + 10 = 49.
Formula for Perimeter of Heptagon - π = π + π + π + π + π + π + π.
Let’s consider another example of a heptagon with side lengths, π = 3, π = 4, π = 5, π = 6, π = 7, π = 8, and π = 9.
So the perimeter of the heptagon will be: π = π + π + π + π + π + π + π = 3 + 4 + 5 + 6 + 7 + 8 + 9 = 42.
How to Calculate the Perimeter of Heptagon
To find the perimeter of a heptagon, we just need to apply the given formula and sum all the sides of the heptagon.
For instance, a given heptagon has sides of a = 2, b = 2, c = 3, d = 3, e = 4, f = 4, g = 5. Perimeter = sum of all sides = 2 + 2 + 3 + 3 + 4 + 4 + 5 = 23 cm. Example Problem on Perimeter of Heptagon
For finding the perimeter of a heptagon, we use the formula, π = π + π + π + π + π + π + π.
For example, let’s say, a = 7 cm, b = 6 cm, c = 5 cm, d = 4 cm, e = 3 cm, f = 2 cm, and g = 1 cm.
Now, the perimeter = sum of all sides = 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 cm
Therefore, the perimeter of the heptagon is 28 cm.
Tips and Tricks for Perimeter of Heptagon
Learning some tips and tricks makes it easier for children to calculate the perimeter of heptagons.
Here are some tips and tricks given below:
- Always remember that a heptagon's perimeter is simply the sum of the seven sides of the shape. For that, use the formula, π = π + π + π + π + π + π + π.
- Calculating the perimeter of a heptagon starts by determining the length of each side using the distance formula.
- The distance formula is: Distance = √((x2-x1)² + (y2-y1)²).
- Here, (x1, y1) and (x2, y2) indicate the positions of two points that make out a heptagon’s side.
- They can be found by adding the lengths of seven sides after they are calculated.
- To reduce the confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of heptagons. After that, apply the formula to each heptagon.
- To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture.
- If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter.
- Area-related calculations often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Heptagon
Did you know that while working with the perimeter of a heptagon, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly assuming all sides are equal, leading to inaccurate calculations.
Remember that not all heptagons are regular (with all sides equal).
Ensure you add up each individual side length to find the correct perimeter.
Mistake 2
Confusing the perimeter with the area, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the heptagon’s sides, while the area, in square units, represents the space inside the heptagon.
Mistake 3
Assuming the heptagon is regular when it could be irregular, which affects the perimeter calculation.
A regular heptagon has all sides of equal length, but an irregular heptagon does not.
Always check the side lengths before calculating the perimeter.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your heptagon.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw a heptagon to accurately identify the side lengths.
Perimeter of Heptagon Examples
Problem 1
A garden plot is in the shape of a heptagon with a perimeter of 56 meters, and six of its sides each measure 7 meters. To find out the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 14 meters.
Explanation
Let ‘g’ be the side of the missing side.
And the given perimeter = 56 meters.
Length of the six equal sides = 7 meters each.
Perimeter of heptagon = sum of lengths of seven sides.
56 = 7 + 7 + 7 + 7 + 7 + 7 + g
56 = 42 + g
g = 56 – 42
= 14
Therefore, the missing side is 14 meters.
Problem 2
A rope with a perimeter of 140 meters is reshaped into a regular heptagon. Find the length of each side of the heptagon by dividing the total length by 7.
20 meters
Explanation
Given that the perimeter of the rope is equal to the perimeter of the heptagon formed, here is the solution:
Perimeter of the rope = Total length of the rope Length of the rope used = Perimeter of the heptagon formed
Perimeter of a regular heptagon = 7 × a
140 = 7 × a
140 ÷ 7 = 20 a
= 20
Therefore, the length of each side of the heptagon is 20 meters.
Problem 3
Find the perimeter of a regular heptagon whose sides are 11 cm.
77 cm
Explanation
Perimeter of regular heptagon = 7 × a
P = 7 × 11
= 77
Therefore, the perimeter of the heptagon is 77 cm.
Problem 4
Lucy is designing a heptagonal flower bed in her backyard. She measures the seven sides of the bed: Side A = 5 meters Side B = 4 meters Side C = 6 meters Side D = 5 meters Side E = 7 meters Side F = 4 meters Side G = 6 meters How much fencing should Lucy buy to go around the edge of the flower bed?
Lucy will need 37 meters of fencing to go around the flower bed.
Explanation
The perimeter of a heptagon is the sum of all the seven sides.
Using the formula: P = a + b + c + d + e + f + g
P = 5 + 4 + 6 + 5 + 7 + 4 + 6 = 37 meters.
Problem 5
Find the perimeter of the irregular heptagonal rock.
Sides are a = 3, b = 5, c = 4, d = 6, e = 2, f = 5, g = 4 Perimeter = a + b + c + d + e + f + g = 3 + 5 + 4 + 6 + 2 + 5 + 4 = 29 meters.
Explanation
Each side of the irregular heptagon has a different length.
The entire distance is calculated around the rock to be 29 meters by summing the lengths of the seven sides.
FAQs on Perimeter of Heptagon
1.Evaluate the heptagonβs perimeter if its sides are 2cm, 3cm, 4cm, 5cm, 6cm, 7cm, and 8cm.
2.What is meant by a heptagonβs perimeter?
3.What are the types of heptagons?
4.Which heptagon has all equal sides?
5.How do you find the perimeter of a heptagon when given the side lengths?
Important Glossaries for Perimeter of Heptagon
- Perimeter: The total length of the sides of a shape.
- Heptagon: A polygon with seven sides and seven angles.
- Regular Heptagon: A heptagon with all sides and angles equal.
- Irregular Heptagon: A heptagon with sides and angles of different lengths and measures.
- Formula of perimeter: The mathematical expression used to calculate the perimeter of a heptagon is π = π + π + π + π + π + π + π.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
