How to Find the Area and Perimeter of the Semicircle?

The circumference of a semicircle is the length of the arc that is half of the circle’s circumference, and the perimeter of a semicircle is the sum of its circumference and diameter.

Related Topics

• How to Find the Area and Circumference of Circles?

A step-by-step guide to finding the area and perimeter of the semicircle

If a circle is cut in half along the diameter, that half-circle is called a semicircle. The two halves are equal in size.

A semicircle can also be called a half-disk and represents a circular paper plate folded into halves.

There is a line of symmetry in the semicircle which is considered the reflection symmetry.

Since a semicircle is half a circle, which is $360°$, the semicircle arc is always $180°$.

Area of a semicircle

The area of a circle refers to the area or interior space of the circle. Since we know that a semicircle is half a circle, the area of a semicircle will be half the area of a circle.

Area of a semicircle $=\color{blue}{\frac{πR^2}{2}}$

where,

$R$ is the radius of the semicircle

Circumference of a semicircle

The circumference of a semicircle is defined as the measurement of the arc that forms a semicircle. It does not include the length of the diameter. The circumference of a semicircle is half of the circle’s circumference.

Circumference of a semicircle $=\color{blue}{\frac{2πR}{2}= πR}$

Semicircle perimeter

The perimeter of a semicircle is the sum of its circumference and diameter. To calculate the perimeter of a semicircle, we need to know the diameter or radius of the circle along with the length of the arc. To determine the length of the arc, we need the circumference of a semicircle.

Since the circumference is $C = πR$, where $C$ is the circumference, and $R$ is the radius, we can define the formula for the perimeter of a semicircle which is:

The perimeter of a semicircle $=\color{blue}{(πR + 2R)}$ units, or after factoring the $R$, the perimeter of a semicircle $=\color{blue}{R(π + 2)}$

where,

• $R$ is the radius of the semicircle

Finding the Area and Perimeter of the Semicircle – Example 1:

Find the circumference of a semicircle with a diameter of $10$ units. $π=3.14$

Solution:
The diameter is $=10$ units. So, radius $= \frac{10}{2} = 5$ units.
The formula to calculate the circumference of a semicircle is $πR$. Therefore, by substituting the values of $π$ and radius in this formula, we get:

Circumference $=3.14× 5$ units

Circumference $=15.70$ units

Exercises for Finding the Area and Perimeter of the Semicircle

1.  Calculate the area of a semicircle whose radius is $8$ inches. $π=3.14$
2. Find the circumference of a semicircle with a diameter of $46$ inches. $π=3.14$
3. What is the area of the semicircle if the perimeter of the semicircle is $156$ units?

1. $\color{blue}{100. 48 \space in^2}$
2. $\color{blue}{118. 22 \space in^2}$
3. $\color{blue}{1446}$