Semicircle – Definition With Examples

What is a Semicircle?

In geometry, a semicircle is defined as a half circle formed by cutting the circle into two halves. It is formed when a line passes through the center and touches the two ends of the circle. This line is called the diameter of the circle.

In the figure above, you can see the diameter dividing the circle into two halves. 

You can also see a blue line drawn from the circle’s center to a point on its edge. The length of the line gives the radius of the circle.

All points on a circle are at an equal distance from its center. So, no matter which point you touch from the center, the radius will always be the same.

Finding the Area of a Semicircle

The area of a semicircle refers to the space inside it or the region enclosed by it. It is half the area of a circle.

Recall that area of a circle is πr², where:

• r is the radius of the circle.
• π is Pi with an approximate value of 22/7 or 3.14.

So, the formula for calculating the area of a semicircle is:

Area = ½ × πr² 

Finding the Perimeter/Circumference of a Semicircle

The perimeter or circumference describes the total length of the boundary of the semicircle. 

You may think that the perimeter of a semicircle is half the perimeter of a circle, but that is not true. 

Half the perimeter of a circle gives the perimeter of the curved part only. You will also have to add the diameter line across the bottom to get the total perimeter.

Recall that the perimeter of a circle is 2πr. 

So, the perimeter of the curved part of the semicircle is ½ × 2πr = πr

Now, let’s add the length of the diameter as well.

So, the total perimeter of the semicircle = πr + d, where d is the diameter.

But, we also know that the diameter of a circle is twice its radius. 

So, substituting the diameter with the radius in the above equation, we get,

The perimeter of semicircle = πr + 2r

Or, perimeter = r (π + 2)

Solved Examples

Example 1: A circle has a diameter of 14 cm. Find the area of the semicircle. (Use π = 22/7)

Solution:

Given: Diameter of a circle = 14 cm

Radius = Diameter/2 = 14/2 = 7 cm

Now,

Area of the semicircle = ½ × πr²

= ½ × 22/7 × 7 ×7

= 77 cm²

Example 2: A semicircle has a diameter of 28 cm. Find its perimeter. (Use π = 22/7)

Solution:

Given: Diameter of the semicircle = 28 cm

Radius = Diameter/2 = 28/2 = 14 cm

Now, 

Perimeter of a semicircle = πr + 2r

= 22/7 × 14 + 2 × 14

= 44 + 28

= 72 cm

Example 3: The diameter of a semicircle is 7 cm. Find the perimeter of its curved surface. (Use π = 22/7)

Solution:

Given: The diameter of the circle is 7 cm

Radius = 7/2 cm

Now, 

The perimeter of the curved surface of semicircle = ½ × 2πr

= ½ × 2 × 22/7 × 7/2

= 11 cm

Practice Problems

Frequently Asked Questions