# 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 πR^{2} 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 = πR ^{2}/ 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,

### 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 r^{2})

Area = (π × 6^{2})/2

= 36 π/2

= 18 π in^{2}

**Answer: **The area of the semicircle is 18π in^{2}.

**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.

## FAQs on Semicircle Formulas

### What is the Area of a Semicircle Formula?

The area of a semi-circle refers to the total amount of inner space of the semi-circle. It is expressed as 'Area of a semicircle formula = πR^{2}/ 2 square units',

where,

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

### What is the Perimeter of a Semicircle Formula?

The perimeter of a semicircle formula is defined as the sum of half of the circumference of the circle and the diameter of a circle. It is expressed as,

- The circumference of a circle is C = πd or C = 2πR.
- The perimeter of a semicircle formula = (πR + 2R) units, or R(π + 2).

where,

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

### What are the Formulas of Semicircle in Geometry?

There are two important formulas of semicircle in geometry which are given below:

- The formula to calculate the area of a semicircle with radius 'r' is given as 1/2 × (πr
^{2}) square units. - The formula to calculate the perimeter of a semicircle with radius 'r' and diameter 'd' is given as πr + d units.

### What is the Circumference of a Semicircle Formula?

The formula of the circumference of a semicircle is πR units. It is the length of the curved edge of the semicircle which is exactly half of the circumference of a circle.

### What is the Formula for Finding the Diameter of a Semicircle?

The diameter of a semicircle can be easily found if any of the following values are known: Area, perimeter, or circumference. If A is the area of the semicircle, then the diameter (d) = √(8A/π) units. If P is the perimeter, then diameter (d) of semicircle formula = 2P/(π + 2) units. And, if C is the circumference, then the diameter (d) = 2C/π units.

### What is the Difference Between the Area of a Circle and Semicircle Formulas?

The area of the circle formula is expressed as A = πr^{2}. Whereas, the area of the semicircle is half the area of the circle. Therefore, the area of the semicircle is πr^{2}/2, where 'r' is the radius. The area of a semicircle is expressed in square units like in^{2}, cm^{2}, m^{2}, yd^{2}, ft^{2}, etc.

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