# How to Find the Area and Perimeter of the Semicircle?

A semicircle is a semicircle. It is a two-dimensional shape that is formed when a circle is cut into two equal parts. In this step-by-step guide, you will learn 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.

## A step-by-step guide tofinding 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 $$180°$$.

The image below shows a semicircle $$PQR$$ along the arc and the diameter $$(PQ)$$ with both endpoints. Here, point $$J$$ is the center, and $$PJ$$ and $$JQ$$ are the radii of the semicircle.

### 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 forFinding 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. $$\color{blue}{1446}$$

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