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.

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

Semicircles

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.DescriptionFormula
1Perimeter of Semicircle formula or
Circumference of Semicircle Formula
\displaystyle C=\pi r+d
or
\displaystyle C=\pi r+2r
2Area of Semicircle formula \displaystyle A=\frac{{\pi {{r}^{2}}}}{2}
3Equation of a Semicircley = {y_0} + \sqrt {{r^2} - {{(x - {x_0})}^2}}
or
y = {y_0} - \sqrt {{r^2} - {{(x - {x_0})}^2}}

Frequently Asked Questions (FAQ)

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

The half of a semicircle is called a quadrant.

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

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

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 

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:

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

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