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Last updated on September 9, 2025

Perimeter of Semicircle

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The perimeter of a shape is the total length of its boundary. The perimeter of a semicircle is the sum of the half circumference of the circle and its diameter. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a semicircle.

Perimeter of Semicircle for US Students
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What is the Perimeter of a Semicircle?

The perimeter of a semicircle is the total length of its curved edge and the straight edge (diameter). By adding the half circumference of the circle and the diameter, we get the perimeter of the semicircle.

 

The formula for the perimeter of a semicircle is 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ, where r is the radius of the semicircle. For instance, if a semicircle has a radius of r = 5, then its perimeter is P = πœ‹ × 5 + 2 × 5 = 5πœ‹ + 10.

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Formula for Perimeter of Semicircle - 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ.

Let’s consider another example of a semicircle with a radius of r = 7.

 

So the perimeter of the semicircle will be: 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ = πœ‹ × 7 + 2 × 7 = 7πœ‹ + 14.

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How to Calculate the Perimeter of Semicircle

To find the perimeter of a semicircle, we just need to apply the given formula and sum the half circumference and diameter. For instance, a given semicircle has a radius of r = 4.

 

Perimeter = half circumference + diameter = πœ‹ × 4 + 2 × 4 = 4πœ‹ + 8.

 

Example Problem on Perimeter of Semicircle -

 

For finding the perimeter of a semicircle, we use the formula, 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ.

 

For example, let’s say, r = 3 cm.

 

Now, the perimeter = half circumference + diameter = πœ‹ × 3 + 2 × 3 = 3πœ‹ + 6 cm.

 

Therefore, the perimeter of the semicircle is 3πœ‹ + 6 cm.

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Tips and Tricks for Perimeter of Semicircle

Learning some tips and tricks makes it easier for children to calculate the perimeter of semicircles. Here are some tips and tricks given below:

 

  • Always remember that a semicircle's perimeter is the sum of the half circumference and its diameter. For that, use the formula, 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ.
     
  • Calculating the perimeter of a semicircle starts by determining the radius.If the diameter is given, remember that radius = diameter/2.
     
  • To reduce confusion, specifically arrange the indicated radius lengths if you need the perimeter of a group of semicircles. After that, apply the formula to each semicircle.
     
  • To avoid mistakes when adding the perimeter, make sure the radius is precise and constant for common uses like gardening and architecture.
     
  • If you are given the full circumference of the circle from which the semicircle is derived, remember that half of it is used for the semicircle's curved part.
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Common Mistakes and How to Avoid Them in Perimeter of Semicircle

Did you know that while working with the perimeter of a semicircle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Mistake 1

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Incorrectly using the formula for the circle's circumference instead of the semicircle's perimeter.

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Remember that the perimeter of a semicircle includes the half circumference plus the diameter, not just the circumference.

Mistake 2

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Students may confuse the concepts of area and perimeter, leading to incorrect calculations.

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It is important to note that the perimeter, calculated in linear units, is the total length of the semicircle’s boundary, while the area, in square units, represents the space inside the semicircle.

Mistake 3

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Using the diameter instead of the radius in the formula, resulting in inaccurate calculations.

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Always be careful to use the radius in the formula 𝑷 = πœ‹π‘Ÿ + 2π‘Ÿ. If the diameter is given, divide it by 2 to find the radius.

Mistake 4

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Using the wrong values for the radius or misreading a problem.

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Double-check the problem and ensure that you're using the correct radius for your semicircle.

Mistake 5

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Misunderstanding or misidentifying the radius or diameter that is given in a problem outline.

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Before starting the calculations, make sure that you understand the problem and, if it's possible, try to sketch a semicircle to accurately identify the given dimensions.

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Perimeter of Semicircle Examples

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Problem 1

A garden has a semicircular path with a radius of 10 meters. To find out the perimeter of this path, use the formula for the perimeter of a semicircle.

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Perimeter = 10πœ‹ + 20 meters.

Explanation

Let ‘r’ be the radius of the semicircle.

Given radius = 10 meters.

Perimeter of semicircle = πœ‹r + 2r. = πœ‹ × 10 + 2 × 10 = 10πœ‹ + 20 meters.

Therefore, the perimeter of the semicircular path is 10πœ‹ + 20 meters.

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Problem 2

A wire with a total length of 50Ο€ inches is used to form a semicircle. Find the radius of the semicircle.

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The radius of the semicircle is 25 inches.

Explanation

Given that the total length of the wire forms the perimeter of the semicircle:

Perimeter of semicircle = πœ‹r + 2r 50π = πœ‹r + 2r 50 = r(πœ‹ + 2) r = 50 / (πœ‹ + 2) r = 25 inches.

Therefore, the radius of the semicircle is 25 inches.

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Problem 3

Find the perimeter of a semicircle whose radius is 6 cm.

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The perimeter of the semicircle is 6πœ‹ + 12 cm.

Explanation

Perimeter of semicircle = πœ‹r + 2r P = πœ‹ × 6 + 2 × 6 P = 6πœ‹ + 12 cm.

Therefore, the perimeter of the semicircle is 6πœ‹ + 12 cm.

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Problem 4

A semicircular arch has a diameter of 16 meters. How much material is needed to go around the edge of the arch?

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32 + 8πœ‹ meters of material is needed.

Explanation

The radius of the semicircle is half of the diameter:

Radius = 16 / 2 = 8 meters.

Perimeter of semicircle = πœ‹r + 2r P = πœ‹ × 8 + 2 × 8

P = 8πœ‹ + 16 meters.

Therefore, 32 + 8πœ‹ meters of material is needed to go around the arch.

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Problem 5

Find the perimeter of a semicircular pond with a radius of 11 meters.

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The perimeter of the semicircular pond is 11π + 22 meters.

Explanation

Perimeter of semicircle = πœ‹r + 2r P = πœ‹ × 11 + 2 × 11 P = 11πœ‹ + 22 meters.

Therefore, the perimeter of the semicircular pond is 11πœ‹ + 22 meters.

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FAQs on Perimeter of Semicircle

1.Evaluate the perimeter of a semicircle if its radius is 4 cm.

Perimeter of semicircle = πœ‹r + 2r, Hence P = πœ‹ × 4 + 2 × 4 = 4πœ‹ + 8 cm.

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2.What is meant by a semicircle’s perimeter?

The total length around a semicircle’s boundary is its perimeter. In other words, the perimeter of a semicircle is the sum of its half circumference and diameter.

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3.What is the difference between a circle and a semicircle?

A circle is a closed shape with all points equidistant from the center, while a semicircle is half of a circle formed by cutting it along its diameter.

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4.How do you calculate the radius if the perimeter is given?

Rearrange the formula for the perimeter of a semicircle to solve for the radius: 𝑷 = πœ‹r + 2r, solve for r.

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5.Which formula is used for the perimeter of a semicircle?

The formula used for the perimeter of a semicircle is 𝑷 = πœ‹r + 2r.

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Important Glossaries for Perimeter of Semicircle

  • Perimeter: The total length of the boundary of a shape.

 

  • Semicircle: Half of a circle formed by cutting a whole circle along its diameter.

 

  • Radius: The distance from the center of a circle to any point on its circumference.

 

  • Diameter: The longest straight line that passes through the center of a circle or semicircle, connecting two points on the circumference.

 

  • Formula of perimeter: The mathematical expression used to calculate the perimeter of a semicircle is 𝑷 = πœ‹r + 2r.
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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.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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