# Semicircles

## 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:

### 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, 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  or

### 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:
If the Radius of Semicirlce is given:

### How to find area of semicircle?

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