Last updated on July 25th, 2025
The perimeter of a shape is the total length of its boundary. The sum of all five sides is called the perimeter of a pentagon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a pentagon.
The perimeter of a pentagon is the total length of its five sides. By adding the length of all five sides, we get the perimeter of the shape. The formula for the perimeter of a pentagon is π· = π + π + π + π + π, where a, b, c, d, and e are the sides of the pentagon. For instance, if a pentagon has sides, a = 5, b = 7, c = 6, d = 9, and e = 4, then its perimeter is p = 5 + 7 + 6 + 9 + 4 = 31.
Letβs consider another example of a pentagon with side lengths, π = 11, π = 8, π = 10, π = 7, and π = 9. So the perimeter of the pentagon will be: π· = π + π + π + π + π = 11 + 8 + 10 + 7 + 9 = 45.
To find the perimeter of a pentagon, we just need to apply the given formula and sum all the sides of the pentagon. For instance, a given pentagon has the sides of a = 6, b = 5, c = 5, d = 6, and e = 8. Perimeter = sum of all sides = 6 + 5 + 5 + 6 + 8 = 30 cm. Example Problem on Perimeter of Pentagon - For finding the perimeter of a pentagon, we use the formula, π· = π + π + π + π + π. For example, letβs say, a = 7 cm, b = 9 cm, c = 4 cm, d = 5 cm, and e = 6 cm. Now, the perimeter = sum of all sides = 7 + 9 + 4 + 5 + 6 = 31 cm. Therefore, the perimeter of the pentagon is 31 cm.
Learning some tips and tricks makes it easier for children to calculate the perimeter of pentagons. Here are some tips and tricks given below: Always remember that a pentagon's perimeter is simply the sum of the five sides of the shape. For that, use the formula, π· = π + π + π + π + π. Calculating the perimeter of a pentagon starts by determining the length of each side using the distance formula. The distance formula is: Distance = β((x2-x1)Β² + (y2-y1)Β²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make up a pentagonβs side. They can be found by adding the lengths of five sides after they are calculated. To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of pentagons. After that, apply the formula to each pentagon. 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.
Did you know that while working with the perimeter of a pentagon, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
A garden plot is shaped like a pentagon and has a perimeter of 60 meters. Four sides measure 12 meters each. To find out the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 12 meters.
Let βeβ be the side of the missing side. And the given perimeter = 60 meters. Length of the four equal sides = 12 meters. Perimeter of pentagon = sum of lengths of five sides. 60 = 12 + 12 + 12 + 12 + e 60 = 48 + e e = 60 β 48 = 12 e = 12 Therefore, the missing side is 12 meters.
A wire with a perimeter of 100 inches is reshaped into a regular pentagon. Find the length of each side of the pentagon and divide the total length by 5.
20 inches
Given that the perimeter of a wire is reshaped into a regular pentagon, here is the solution: Perimeter of the wire = Total length of the wire Length of the wire used = Perimeter of the pentagon formed Perimeter of a regular pentagon = 5 Γ a 100 = 5 Γ a 100 Γ· 5 = 20 a = 20 Therefore, the length of each side of the pentagon is 20 inches.
Find the perimeter of a regular pentagon whose sides are 8 cm.
40 cm
Perimeter of pentagon = a + b + c + d + e P = 8 + 8 + 8 + 8 + 8 = 40 Therefore, the perimeter of the pentagon is 40 cm.
Emma is planning a pentagon-shaped flower bed in her backyard. She measures the five sides of the bed: Side A = 10 meters Side B = 8 meters Side C = 12 meters Side D = 9 meters Side E = 11 meters How much fencing should Emma buy to go around the edge of the flower bed?
Emma will need 50 meters of fencing to go around the flower bed.
The perimeter of a pentagon is the sum of all the five sides. Using the formula: P = a + b + c + d + e P = 10 + 8 + 12 + 9 + 11 = 50 meters.
Find the perimeter of an irregular pentagon with side lengths a = 14, b = 10, c = 9, d = 8, and e = 13 meters.
Perimeter = a + b + c + d + e = 14 + 10 + 9 + 8 + 13 = 54 meters.
Each side of the irregular pentagon has a different length. The entire distance is calculated around the pentagon to be 54 meters by summing the lengths of the five sides.
Perimeter: The total length of the sides of a shape. Pentagon: A polygon with five sides and five angles. Regular Pentagon: A pentagon with all equal sides and angles. Irregular Pentagon: A pentagon with sides and angles of different lengths. Formula of perimeter for a pentagon: The mathematical expression used to calculate the perimeter of a pentagon is π· = π + π + π + π + π.
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.
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