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Last updated on September 9, 2025
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.
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 π· = ππ + 2π, 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 × 5 + 2 × 5 = 5π + 10.
Let’s consider another example of a semicircle with a radius of r = 7.
So the perimeter of the semicircle will be: π· = ππ + 2π = π × 7 + 2 × 7 = 7π + 14.
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 × 4 + 2 × 4 = 4π + 8.
Example Problem on Perimeter of Semicircle -
For finding the perimeter of a semicircle, we use the formula, π· = ππ + 2π.
For example, let’s say, r = 3 cm.
Now, the perimeter = half circumference + diameter = π × 3 + 2 × 3 = 3π + 6 cm.
Therefore, the perimeter of the semicircle is 3π + 6 cm.
Learning some tips and tricks makes it easier for children to calculate the perimeter of semicircles. Here are some tips and tricks given below:
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:
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.
Perimeter = 10π + 20 meters.
Let ‘r’ be the radius of the semicircle.
Given radius = 10 meters.
Perimeter of semicircle = πr + 2r. = π × 10 + 2 × 10 = 10π + 20 meters.
Therefore, the perimeter of the semicircular path is 10π + 20 meters.
A wire with a total length of 50Ο inches is used to form a semicircle. Find the radius of the semicircle.
The radius of the semicircle is 25 inches.
Given that the total length of the wire forms the perimeter of the semicircle:
Perimeter of semicircle = πr + 2r 50π = πr + 2r 50 = r(π + 2) r = 50 / (π + 2) r = 25 inches.
Therefore, the radius of the semicircle is 25 inches.
Find the perimeter of a semicircle whose radius is 6 cm.
The perimeter of the semicircle is 6π + 12 cm.
Perimeter of semicircle = πr + 2r P = π × 6 + 2 × 6 P = 6π + 12 cm.
Therefore, the perimeter of the semicircle is 6π + 12 cm.
A semicircular arch has a diameter of 16 meters. How much material is needed to go around the edge of the arch?
32 + 8π meters of material is needed.
The radius of the semicircle is half of the diameter:
Radius = 16 / 2 = 8 meters.
Perimeter of semicircle = πr + 2r P = π × 8 + 2 × 8
P = 8π + 16 meters.
Therefore, 32 + 8π meters of material is needed to go around the arch.
Find the perimeter of a semicircular pond with a radius of 11 meters.
The perimeter of the semicircular pond is 11π + 22 meters.
Perimeter of semicircle = πr + 2r P = π × 11 + 2 × 11 P = 11π + 22 meters.
Therefore, the perimeter of the semicircular pond is 11π + 22 meters.
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.
: She has songs for each table which helps her to remember the tables