Semicircle Formulas

Half a portion of any circle is known as a semicircle and is formed by cutting a whole circle along the diameter. Various parameters related to a semi-circle like a diameter, area, the perimeter can be calculated using semicircle formulas. The diameter of a circle divides the circle into two equal semicircles. The area of any semicircle is half of the area of a circle. Let us understand the semicircle formulas using solved examples in the following sections.

What are Semicircle Formulas?

The semicircle formulas include the formulas to calculate the area, perimeter, and circumference of a semicircle. These formulas are based on the fact that a semicircle is half a portion of a full circle.

Area of a Semicircle Formula

Since we know that a semicircle is half a circle, the semicircle area will be half of the area of a circle. So, the area of a circle is πR² where R is the radius of the circle. The area of a semi-circle refers to the region or inner space of the semi-circle. Hence,

Area of a semicircle formula = πR²/ 2 square units.

where,

• r = R is the radius of a semicircle
• π(pi) is 22/7 or 3.142 approximately.

Perimeter of a Semicircle Formula

The perimeter of a semicircle formula is used to calculate the perimeter of a semicircle. We must know either the diameter or radius of a circle along with the length of the arc. To evaluate the length of the arc of the semicircle, we must calculate the circumference of a circle.

• The circumference of a circle is C = πd or C = 2πr.
• Using the value of C, we can determine the formula for the perimeter of a semicircle which is calculated as the sum of half of the circumference of the circle and diameter of a circle.
• The perimeter of a semicircle formula = (πR + d) or (πR + 2R), or R(π + 2) units.

where,

• R = radius of a semicircle
• π(pi) is 22/7 or 3.142 approximately, and,
• d = Diameter of a semicircle.

Circumference of a Semicircle Formula

The circumference of a semicircle is defined as the length of the arc around the semicircle. It is half of the circumference of a circle. The difference between the circumference and perimeter of a semicircle is that the circumference is only the length of the arc which is the curved portion on the boundary, while the perimeter of the semicircle includes circumference as well as diameter.

Circumference of semicircle formula = πR units

where,

• R = radius of the semicircle
• π(pi) is 22/7 or 3.142 approximately.

Let us see how to use these semicircle formulas in the following section.

Examples on Semicircle Formula

Let us take a look at a few examples to better understand the formulas of the semicircle.

Example 1: Using the semicircle formula calculate the area of the semicircle whose diameter is 12 in. Express your answer in terms of π.

Solution:

To find: The area of the semicircle,
Given: Diameter of the semicircle = 12 in
Radius of semicircle = 12/2 = 6 in
Using semicircle formulas,
Area of Semicircle = 1/2 × (π r²)
Area = (π × 6²)/2
= 36 π/2
= 18 π in²

Answer: The area of the semicircle is 18π in².

Example 2: If the radius of a semicircle is 7 units, then using the semicircle formula find its perimeter.

Solution:

To find: The perimeter of a semicircle
Given:
The radius of semicircle = 7 units
Using the perimeter of a semicircle formula,
Perimeter of a semicircle = πr + d = πr + 2r
= (7 × 22/7 + 14) units
= (22 + 14) units

Answer: The perimeter of the semicircle is 36 units.

Example 3: Using the semicircle formulas, calculate the circumference of a semi-circle whose diameter is 8 units.

Solution:

To find: The circumference of a semicircle
Given:
The diameter of semicircle = 8 units
Radius = 8/2 = 4 units
Using the circumference of a semicircle formula,
Circumference of a semicircle = πr units
C = (3.14) × (4)
C = 12.56 units

Answer: The circumference of the semicircle is 12.56 units.