# Perimeter of a Semicircle – Definition, Formula, Examples, Facts

## What Is the Perimeter of a Semicircle?

Perimeter of a semicircle is the total length of its boundary, which is composed of half of the circumference of the circle and the length of the diameter.

Perimeter of a semicircle $= \pi r + 2r$

What is a semicircle?

When a circle is divided into two equal halves by the diameter, each half is called a semicircle. A semicircle is simply a half circle.

What is the perimeter?

The perimeter describes the total length of the boundary of a 2D figure. The perimeter of a circle is known as its circumference.

## Perimeter of a Semicircle Formula

Perimeter of a semicircle $=$ half of the circumference of the circle $+$ diameter

Perimeter of a semicircle $= \pi r + d$

Perimeter of a semicircle $= \pi r + 2r$

where “r” is the radius of the circle.

## How to Find the Perimeter of a Semicircle

Let’s understand how to find the perimeter of a half circle.

Step 1: Find the half the perimeter (circumference of the circle).

Step 2: Find the length of the diameter.

Step 3: Add the values obtained in step 1 and step 2.

Step 4: Give the appropriate unit based on the unit of the radius.

## Perimeter of a Semicircle Is Not Half the Perimeter of the Circle

Semicircle is half of a circle, but the perimeter of a semicircle is not half of the perimeter of the circle.

Half the perimeter of a circle only represents the curved part of the semicircle.

Perimeter of a circle $= 2\pi r$.

Half the perimeter of the circle $= \frac{1}{2} \times 2\pi r = \pi r$

The semicircle also has diameter as part of its boundary. We need to add the length of the diameter to get the total perimeter of the semicircle.

Length of the diameter $= d = 2r$              d is the diameter, r is the radius

• Perimeter of the semicircle $= \pi r + d$
• Perimeter of the semicircle $= \pi r + 2r$
• Perimeter of the semicircle $= r (\pi + 2)$

Let’s visualize this to get a better idea!

## Finding the Perimeter of a Semicircle When Area Is Given

Area of a circle $= \pi r^{2}$

Semicircle is half the circle.

So, area of semicircle $= \frac{1}{2} \times \pi r^{2}$ ….(1)

Suppose the area of the semicircle is 77 square inches.

We will find the radius using the formula (1).

So, $= \frac{1}{2} \times \pi r^{2} = 77$

$\pi r^{2} = 154$

$\frac{22}{7} \times r \times r = 154$

$r = 7$ inches

Substitute $r = 7$ in the formula of perimeter of a semicircle.

In this case, we get

Perimeter of semicircle $= \pi r + 2r$

Perimeter of semicircle $= \frac{22}{7} \times 7 + 2 \times 7$

Perimeter of semicircle $= 22 + 14$

Perimeter of semicircle $= 36$ inches

## Facts about Perimeter of a Semicircle

• Area of a circle is half the area of a circle, but that’s not the case with the perimeter (circumference) of a semicircle.
• Perimeter of a quarter circle $=$ One fourth of the circumference of the circle $+$ twice the radius.

## Solved Examples on Perimeter of a Semicircle

1. Find the perimeter of the given semicircle.

Solution:

Radius $(r) = 0.7$ inches

Perimeter $= \pi r + 2r$

Perimeter $= \frac{22}{7} \times 0.7 + 2 \times 0.7$

Perimeter $= 2.2 + 1.4$

Perimeter $= 3.6$ inches

2. What is the perimeter of a semicircle with diameter 21 inches?

Solution:

Diameter $= 21$ inches

Radius $(r) = \frac{Diameter}{2} = 10.5$ inches

Perimeter $= \pi r + d$

Perimeter $= \frac{22}{7} \times 10.5 + 21$

Perimeter $= 33 + 21$

Perimeter $= 43$ inches

3. If the perimeter of the semicircle is 7.2 feet, then find the radius of the circle.

Solution:

Perimeter of the semicircle $= 7.2$ feet

Let the radius of the semicircle be r feet.

$r(\pi + 2) = 7.2$

$r(\frac{22}{7} + 2) = 7.2$

$r(\frac{22 + 14}{7}) = 7.2$

$r \times \frac{36}{7} = 7.2$

$r = \frac{7.2 \times 7}{36}$

$r = 1.4$ feet

4. If the perimeter of the semicircle is 28.8 inches, find the diameter of the circle.

Solution:

Perimeter of the semicircle $= 28.8$ inches

Let the radius of the semicircle be r inches and diameter be d inches.

$r (\pi + 2) = 28.8$

$r (\frac{22}{7} + 2) = 28.8$

$r (\frac{22 + 14}{7}) = 28.8$

$r\times \frac{36}{7} = 28.8$

$r = \frac{28.8 \times 7}{36} = 5.6$ inches

We know that

$d = 2r$

$\Rightarrow d = 2 \times 5.6 = 11.2$ inches

5. If the area of the circle is 7546 square units, what is the perimeter of the semicircle?

Solution:

Area of the circle $= \pi r^{2}$

$7546 = \pi r^{2}$

$7546 = \frac{22}{7} \times r \times r$

$\frac{7546 \times 7}{22} = r \times r$

$2401 = r^{2}$

$r = 49$ units

## Practice Problems on Perimeter of a Semicircle

1

### The perimeter of a half circle is given by

$r (\pi + 2)$ units
$2r( \pi + 2)$ units
$d(\pi + 4)$ units
$d(\pi + 1)$ units
CorrectIncorrect
Correct answer is: $r (\pi + 2)$ units
Perimeter of the semicircle $= \pi r + 2r = r (\pi + 2)$
2

### If the radius of the circle is 3.5 inches, which of the following is the perimeter of the semicircle?

18 inches
20 inches
36 inches
14.5 inches
CorrectIncorrect
Radius $(r) = 3.5$ inches
Perimeter of the semicircle $= \pi r + 2r$
Perimeter of the semicircle $= (\frac{22}{7} \times 3.5) + (2 \times 3.5)$
Perimeter of the semicircle $= 11 + 7 = 18$ inches
3

### What is the perimeter of a semicircle with diameter 10 feet $(\pi = 3.14)$?

41.4 inches
51.4 inches
55.4 inches
63.8 inches
CorrectIncorrect
Radius $(r) = 3.5$ inches
Perimeter of the semicircle $= \pi r + 2r$
Perimeter of the semicircle $= 3 \times .14 \times 10 + 2 \times 10$
Perimeter of the semicircle $=31.4 + 20 = 51.4$ inches
4

### If the perimeter of the semicircle is 10.8 feet, find the radius of the semicircle.

5.6 inches
4.2 inches
3.7 inches
2.1 inches
CorrectIncorrect
Perimeter of the semicircle $= 10.8$ inches
Let the radius of the semicircle be r inches.
$r ( \pi + 2) = 10.8$
$r (\frac{22}{7} + 2) = 10.8$
$r ( \frac{22 + 14}{7}) = 10.8$
$r \times \frac{36}{7} = 10.8$
$r = \frac{10.8 \times 7}{36} = 2.1$ inches
5

### The perimeter of the semicircle with radius 1 unit is _____.

$\pi$ units
$2(\pi + 2)$ units
$(\pi + 2)$ units
$(\pi + 4)$ units
CorrectIncorrect
Correct answer is: $(\pi + 2)$ units
Perimeter of the semicircle $= r(\pi + 2)$
If $r = 1$, the perimeter $= (\pi + 2)$ unit

Perimeter for a 2-dimensional shape is the total distance around the respective shape whereas the area for a 2-dimensional shape is the region enclosed within the perimeter of the given shape.

Area of the circle with radius r units $=\pi r^{2}$ square units

Yes. The angle in a semicircle is $180^{\circ}$ as the semicircle is half a circle and the angle in a circle is $360^{\circ}$.

Half the semicircle is known as a quadrant or the quarter of a circle.

No. A semicircle is made up of one curved and one straight line segment, but a polygon is made of only straight line segments.

Perimeter of a semicircle $= \pi r + 2r$, where r is the radius of the circle.

No. The circumference of a semicircle is not half the circumference of the circle.