Perimeter Of Semicircle - Formula, Definition, Examples - Cuemath

Perimeter of Semicircle

The perimeter of a semicircle is the total length of its boundary. It is easy to calculate the perimeter of shapes that have straight edges, like in the case of a square, where all the sides can be simply added. However, the perimeter of a semicircle has a different formula since a semicircle is half of a circle, and it consists of a curved and a straight boundary. Let us learn how to calculate the perimeter of semicircle using the perimeter of semicircle formula in this lesson.

1.	What is the Perimeter of Semicircle?
2.	Perimeter of Semicircle Formula
3.	How to Find the Perimeter of Semicircle?
4.	FAQs on Perimeter of Semicircle

What is the Perimeter of Semicircle?

The perimeter of a semicircle, which is also known as the circumference of a semicircle, is defined as the total length of its boundary. It is calculated by adding the length of the diameter and half the circumference of the original circle. The unit of the perimeter of the circle is expressed in linear units like inches, feet, meters or centimeters, etc. It can also be referred to as the perimeter of half circle.

Circumference of a Semicircle

The circumference of a semicircle is another name for the perimeter of a semi circle. So, it is the length of the boundary of half of the circle's circumference and the diameter of the semi circle.

Perimeter of Semicircle Formula

Observe the following semicircle where AB is the diameter of the semicircle marked as 'd' and OM is the radius marked as 'r'.

The perimeter of the semicircle is given as P = Half of the Circumference of the original circle + Length of Diameter.

We know that Circumference of circle = 2πr

Half of the circumference of the circle = (1/2) × 2πr = πr

We know that the length of diameter can also be expressed in terms of radius as = d = 2r

• Therefore, the circumference of semicircle formula in terms of the radius is expressed as, Perimeter of Semi circle = r(π + 2)
• In terms of diameter, the circumference of semicircle formula is expressed as, Perimeter of Semi circle = π(d/2) + d

How to Find the Perimeter of Semicircle?

In order to find the perimeter of a semi circle, we need to check the parameters that are given.

• If the diameter of the semi-circle is given, then we use the formula, Perimeter of Semi circle = π(d/2) + d, where 'd' is the diameter and π = 3.14 or 22/7
• If the radius of the semi-circle is given, then we use the formula, Perimeter of Semi circle = r(π + 2), where 'r' is the radius and π = 3.14 or 22/7
• We know that the diameter is twice the radius of a circle. Therefore, if the diameter is given, we can also find the radius by the formula, radius = diameter/2. Then, we can find the perimeter of the semi circle using this radius, Perimeter of Semi circle = r(π + 2), where 'r' is the radius.
• This applies in the opposite case as well. When the radius is given, we can find the diameter with the formula, diameter = 2 × radius. Then, we can find the perimeter of the semi circle using this diameter, Perimeter of Semi circle = π(d/2) + d, where 'd' is the diameter.

Let us understand this with the help of an example.

Example: Find the circumference of a semicircle whose radius is 7 units. (Use π = 3.14)

Solution: The radius of the semicircle is 7 units.

The perimeter or the circumference of the semicircle can be calculated using the circumference of semicircle formula, P = r(π + 2), where 'r' is the radius.

Here, r = 7. After substituting the values, we get,

Perimeter = P = r(π + 2) ⇒ 7(3.14 + 2) = 35.98 units.

Therefore, the perimeter of the semi-circle = 36 units.