A pentagon is a five-sided polygon with five angles. The perimeter of a pentagon is the total distance around its edges, and calculating this perimeter depends on whether the pentagon is regular (all sides and angles are equal) or irregular (sides and angles are not equal).
In this article, we will discuss the concept of Perimeter of a Pentagon, including examples and steps for finding perimeter of pentagon.
Table of Content
What is a Pentagon?
A pentagon is a five-sided polygon with five angles. The term "pentagon" comes from the Greek words "pente," meaning five, and "gon," meaning angle. Pentagons can be classified into two main types:
- Regular Pentagon
- All sides are of equal length.
- All interior angles are equal, each measuring 108Ā°.
- It is highly symmetrical and has rotational symmetry of order 5.
- Irregular Pentagon
- The sides and angles can have different lengths and measures.
- It lacks the symmetrical properties of a regular pentagon.
Perimeter of a Pentagon
The perimeter of a pentagon is the total length of its five sides.
Formula for Perimeter of a Pentagon
The formula for the perimeter depends on whether the pentagon is regular or irregular.
For Regular Pentagon
P = 5 Ć s
Where s is the length of one side.
Since all sides are of equal length, the perimeter P can be calculated by multiplying the length of one side s by 5.
Irregular Pentagon
\text{Perimeter} = s_1 + s_2 + s_3 + s_4 + s_5
Where s1, s2, s3, s4, and s5ā are the lengths of the sides.
For an irregular pentagon, the perimeter P is the sum of the lengths of all five sides.
How to Calculate the Perimeter of a Pentagon?
For a Regular Pentagon
- Step 1: Determine the length of one side of the pentagon. Let's call this length s.
- Step 2: Multiply the length of the side by 5 to find the perimeter.
For an Irregular Pentagon
- Step 1: Measure the length of each of the five sides of the pentagon. Let's call these lengths s1, s2, s3, s4, and s5.
- Step 2: Add the lengths of all five sides to find the perimeter i.e.,
\text{Perimeter} = s_1 + s_2 + s_3 + s_4 + s_5
Example Calculation for Regular Pentagon
- If each side of the regular pentagon is 8 cm, the perimeter is:
Perimeter = 5 Ć 8 = 40 cm
Example Calculation for Irregular Pentagon
- If the sides of the irregular pentagon are 7 cm, 6 cm, 8 cm, 5 cm, and 9 cm, the perimeter is:
Perimeter = 7 + 6 + 8 + 5 + 9 = 35 cm
Read More,
- Regular Polygon
- Angles in Pentagon
- Area of a Pentagon
- Area of a Pentagon Formula
- Diagonal of a Regular Pentagon
- Area of a Pentagonal Pyramid
- Diagonal of a Regular Pentagon
Solved Examples on Perimeter of a Pentagon
Example 1: Calculate the perimeter of a regular pentagon with each side measuring 10 cm.
Solution:
Identify the length of one side: s = 10 cm
Use the formula for the perimeter of a regular pentagon: Perimeter = 5 Ć s
Calculate the perimeter: Perimeter = 5 Ć 10 = 50 cm
Answer: The perimeter of the regular pentagon is 50 cm.
Example 2: Calculate the perimeter of an irregular pentagon with sides measuring 12 cm, 9 cm, 14 cm, 8 cm, and 11 cm.
Solution:
Identify the lengths of all five sides: s1 = 12 cm, s2 = 9 cm, s3 = 14 cm, s4 = 8 cm, s5 = 11 cm
Use the formula for the perimeter of an irregular pentagon:
\text{Perimeter} = s_1 + s_2 + s_3 + s_4 + s_5 āCalculate the perimeter: Perimeter = 12 + 9 + 14 + 8 + 11 = 54 cm
Answer: The perimeter of the irregular pentagon is 54 cm.
Example 3: A regular pentagon has a perimeter of 75 cm. What is the length of each side?
Solution:
Identify the perimeter: Perimeter = 75 cm
Use the formula for the perimeter of a regular pentagon: Perimeter = 5 Ć s
Rearrange the formula to solve for s: s = Perimeter/5
Calculate the length of each side: s = 75/5 = 15 cm
Answer: Each side of the regular pentagon measures 15 cm.
Practice Problems on Perimeter of a Pentagon
Problem 1: Calculate the perimeter of a regular pentagon with each side measuring 15 cm.
Problem 2: Find the perimeter of an irregular pentagon with sides measuring 8 cm, 12 cm, 5 cm, 10 cm, and 9 cm.
Problem 3: A regular pentagon has a side length of 20 cm. What is its perimeter?
Problem 4: Determine the perimeter of an irregular pentagon with side lengths of 6 cm, 7 cm, 8 cm, 9 cm, and 10 cm.
Problem 5: If the perimeter of a regular pentagon is 55 cm, what is the length of each side?
Problem 6: Calculate the perimeter of an irregular pentagon with the following side lengths: 13 cm, 15 cm, 12 cm, 14 cm, and 16 cm.
Problem 7: The side length of a regular pentagon is 18 cm. Find its perimeter.
Problem 8: An irregular pentagon has sides measuring 9 cm, 11 cm, 8 cm, 10 cm, and 12 cm. What is its perimeter?
Problem 9: A regular pentagon's side length is 25 cm. What is the perimeter?
Problem 10: Determine the perimeter of an irregular pentagon with sides of 5 cm, 7 cm, 10 cm, 6 cm, and 8 cm.
