Table of Contents

## Definition of Semicircles

When a circle is cut into two equal sections by its diameter, then the resulting two sections are called the **Semicircles** of the circle.

As shown in the figure below, the diameter of the circle is PQ. If the circle is cut by its diameter PQ at the points P and Q, then the resulting arcs are called the **Semicircles**.

The full arc of a semicircle is {180^0} or \pi radians.

## Perimeter of Semicircle

We know that a **Semicircle** is formed by half of a circle plus the **Diameter**. The **Perimeter of Semicircle** is also called the **Circumference of Semicircle**. Therefore, the **Perimeter of Semicircle** is defined as the sum of half of the **Perimeter** of full circle and its **Diameter**. The same is given by,

\displaystyle C=\pi r+d

or

\displaystyle C=\pi r+2r

## Area of Semicircle

The **Area of Semicircle** is the half of the area of the full circle. Therefore, the **Area of Semicircle Formula** is given by,

\displaystyle A=\frac{{\pi {{r}^{2}}}}{2}

## Equation of a Semicircle

The equation of a semicircle when it is concave from bottom, with center at ({x_0},{y_0}) is:

y = {y_0} + \sqrt {{r^2} - {{(x - {x_0})}^2}}

If the semicircle is concave from top, then the equation of the semicircle will be:

y = {y_0} - \sqrt {{r^2} - {{(x - {x_0})}^2}}

## Semicircle Formula

The important formulas for** Semicircles** are tabulated below:

Serial No. | Description | Formula |

1 | Perimeter of Semicircle formula or Circumference of Semicircle Formula | \displaystyle C=\pi r+d or \displaystyle C=\pi r+2r |

2 | Area of Semicircle formula | \displaystyle A=\frac{{\pi {{r}^{2}}}}{2} |

3 | Equation of a Semicircle | y = {y_0} + \sqrt {{r^2} - {{(x - {x_0})}^2}} or y = {y_0} - \sqrt {{r^2} - {{(x - {x_0})}^2}} |

## Frequently Asked Questions (FAQ)

### What is semicircle?

When a circle is cut into two equal parts by its diameter, then the resulting two sections are called the semicircles of the circle.

### What is half of a semicircle called?

The half of a semicircle is called a quadrant.

### How do you find the area of a semicircle?

The formula for finding the area of a semicircle is A=(πr²$ )/2$, where, r is the radius of the semicircle.

### Does a semicircle have two right angles?

Yes, a semicircle has two right angles as it can be divided into two quadrants.

### What is the circumference of a semicircle?

The circumference of a semicircle is the summation of half of the circumference of the full circle and its diameter. The formula for finding out the circumference of a semicircle is $C=πr+d$ or $C=πr+2r$

### How to find the perimeter of a semicircle?

The Perimeter of Semicircle can be found out by using the following formula:

If the Diameter of Semicircle is given: $C=πr+d$

If the Radius of Semicirlce is given: $C=πr+2r$

### How to find area of semicircle?

The Area of Semicircle can be found out by using the formula: $A=(πr²)/2 $

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