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.

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.

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

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.

What do you Mean by Perimeter of Semicircle?

The perimeter of a semicircle is defined as the total length of its boundary which is calculated by adding the length of the diameter and half the circumference of the original circle. Its unit is expressed in inches, feet, meters or centimeters. The perimeter of a semicircle is also known as the circumference of the semicircle.

What is the Formula of Perimeter of Semicircle?

The formula for the perimeter of the semicircle is the sum of the length of the diameter and half the circumference of the original circle. In order to find the perimeter of a semi circle, we need to check the parameters that are given and then use the appropriate formula.

• 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

How to Find the Perimeter of a Semicircle?

We can find the perimeter of a semicircle using the following formulas:

• f 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

What is the Perimeter of Semicircle of Radius 7 cm?

If the radius of a semicircle is 7 cm, the perimeter can be calculated with the help of the formula: Perimeter = r(π + 2), where 'r' is the radius and π is equal to 3.14. On substituting the values we get, Perimeter = r(π + 2) = 7(3.14 + 2) = 7 × 5.14 = 35.98 cm.

What is the Difference Between Circumference and Perimeter of Semicircle?

The perimeter of a semicircle and the circumference of a semicircle mean the same. Both of them refer to the total length of the boundary of a semicircle. Hence, circumference is another name for the perimeter of a semicircle.

How to find the Perimeter of Semicircle with Diameter?

If the diameter of a semicircle is given, the perimeter can be calculated with the help of the formula: Perimeter = π(d/2) + d, where 'd' is the diameter of the semicircle and π is equal to 22/7. For example, the diameter of a semicircle is given as 16 units, on substituting the values we get, Perimeter = π(d/2) + d = [π × (16/2)] + 16 = 41.14 units

How to find the Area and Circumference of a Semicircle?

The area of a semicircle can be calculated with the help of the formula, Area = πr² /2, where 'r' is the radius of the semicircle and π is a constant with a value of 22/7. For example, the radius of a semicircle is 7 units, let us substitute the values in the formula, Area = πr² /2 = [(22/7) × 7²] /2 = 77 square units. The circumference of a semicircle can be calculated with the help of the formula, Circumference of semi circle = r(π + 2), where 'r' is the radius and π is equal to 3.14. On substituting the values we get, Perimeter = r(π + 2) = 7(3.14 + 2) = 7 × 5.14 = 35.98 cm.

What is the Circumference of a Semicircle with a Diameter of 8 units?

If the diameter of a semicircle is given, the circumference can be calculated with the help of the formula: Circumference = π(d/2) + d, where 'd' is the diameter of the semicircle and π is equal to 22/7. In this case, the diameter of a semicircle is given as 8 units. On substituting the values we get, Circumference = π(d/2) + d = [π × (8/2)] + 8 = 20.57 units.

How do you find the Radius if the Perimeter of Semicircle is Given?

If the perimeter of a semicircle is given, we can find the radius of the semicircle using the same formula, Perimeter = r(π + 2), where 'r' is the radius and π is equal to 22/7. For example, if the perimeter of a semicircle is 21 units, on substituting the values we get, 21 = r(22/7 + 2). This gives the value of the radius as 4.08 units.

How to Find the Area of Semicircle When the Circumference of Semi circle is Given?

We can find the area of a semicircle when the circumference of the semicircle is given using the following steps:

• Step 1: Find the value of the radius using the formula of the perimeter of the semicircle, P = r(π + 2), and equate it to the value of the perimeter of the semicircle.
• Step 2: Once, the equation is obtained, solve for 'r'.
• Step 3: Use the formula, A = (πr²)/2 to determine the value of the area of the semicircle.

What is the Formula for the Circumference of Semi circle in Terms of the Diameter?

The formula for the circumference of a semicircle is, r(π + 2), where 'r' is the radius. As we know that diameter is twice the value of the radius, thus, d = 2r. The formula for the circumference of a semicircle becomes, C = π(d/2) + d.