Area and Perimeter of a Semi Circle – Definition, Formula, Examples | How to find the Area and Perimeter of a Semicircle?

Area and Perimeter of Semi-circle Problems help the students to explore their knowledge of semi-circle Problems. Solve all the Problems to learn the formula of the Area of the semi-circle and the Perimeter of a semi-circle. To know the definition, Problems with Solutions, Formulas of Semi-circle you can visit our website. We have given the complete Semi-circle concept along with examples. Check out the Area and Perimeter of Semi-circle Problems and know the various strategies to solve problems in an easy and understandable way.

Semi-Circle – Definition

A semi-circle is defined as a half-circle that is formed by cutting a whole circle into two halves along with a diameter line. The Semi-circle has only one line of symmetry which is the reflection symmetry. A line segment is known as the diameter of a circle cuts the circle into two equal semicircles. It is also referred to as half-disk. A semi-circle will be half of the circle that is 360 degrees, the arc of the semicircle always measures 180 degrees. The below figure shows the Semi-circle.

Area and Perimeter of a Semi-Circle – Definitions and Formulas

Area of a Semi-Circle: The area of a semicircle is half of the area of a circle. We know that the area of a circle is πr2. So, the area of a semicircle is,
Area of a Semi-circle = 1/2πr2
where r will be the radius.
The value of π is constant. So, the value is 3.14 or 22/7.

The perimeter of a Semi-Circle: The perimeter of a semicircle is defined as the total length of its boundary. It is also known as the Circumference of a Semicircle. It is calculated as adding the length of the diameter and half the circumference of a circle. The perimeter of a circle unit is expressed in linear units like inches, feet, meters or centimeters and etc.
The Perimeter of a semicircle is, πr+2r.
Where r is the radius and π is a constant value that is 3.14.

The perimeter of the semicircle is P = Half of the Circumference of the original circle + Length of the Diameter.
The Circumference of a circle is 2πr.
The half of the circumference of the circle is 1/2 x the circumference of a circle.
=1/2 x 2πr = πr =π(d/2).
The length of the diameter is d = 2r.
In terms of radius, the circumference of the semicircle is P = C = πr + d = πr + 2r = (π + 2)r
In terms of Diameter, the circumference of a semicircle is P = C = π(d/2) + d.

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Solved Problems on Area and Perimeter of a Semicircle

Problem 1: Find the area of a semicircle. If the perimeter of a semicircle is 122 units. Consider the π value is  22/7.

Solution: 
Given the values in the question,
The perimeter of a semicircle is 122 units.
We know that the area of a semicircle is 1/2(πr2).
Using the perimeter of a semicircle value, find the radius (r) value.
The perimeter of a semicircle is πr + 2r = 122units.
πr + 2r = 122 units.
(22/7+2)r = 122 units
(36/7)r = 122 units
r = (7/36) x 122 = 23.7 units.
Now, we will find the area of a semicircle.
A = 1/2(πr2).
A = (22/7 × (23.72))/2 = (3.14)x(561.6)/2 = 881.7 square units.
Therefore, the area of the semicircle is 881.7 sq. units.

Problem 2: If the radius of a semicircle is 4units, then using the semicircle formula find its perimeter?

Solution: 
As given in the question, the radius of the semicircle is 4units.
Now, we have to find the perimeter of a semicircle using the formula.
The perimeter or circumference of a semicircle is, πr + d = πr + 2r
Substitute the radius (r) value in the above formula, we get
P = πr + 2r =(π+ 2)r = (3.14 + 2)(4) = 20.56 units
Thus, the perimeter of a semicircle is 20.56 units.

Problem 3: Using the below figure, find the Perimeter and Area of a semicircle?

Solution: 
Given in the question, the figure consists of radius value, r = 2cm.
Using the radius value, find the area and perimeter of a semicircle.
We know that the Area of a semicircle is (πr2)/2.
So, the value is, A = {(22/7) (2)2} /2 cm2.
A = (3.14) (4) /2 cm2= 6.28cm2
Now, the perimeter of a semicircle is (π + 2)r.
Substitute the values in the above formula. We get,
P = (π + 2)r = (3.14 + 2)(2) = (5.14)(2) = 10.28 cm.
Thus, the perimeter and area of a semicircle are 6.28cm2 and 10.28 cm.

Problem 4: Find the area of semicircle using the below figure. The below figure consists of a semicircle and equilateral triangle.

Solution: 
As given in the question, the figure consists of a semicircle and triangle.
The radius of a semicircle is 4cm.
We know that the area of a semicircle is 1/2(πr2).
Substitute the given values in the above formula, we get
Now, we will the area of a semicircle.
A = 1/2(πr2).
A = (22/7 × (42))/2 = (3.14)x(16)/2 = 25.12 cm2.
Therefore, the area of the semicircle is cm2.

FAQ’S on Area and Perimeter of a Semicircle

1. What are the steps for finding the perimeter of a semicircle?

The steps to determine the perimeter of a semicircle are given below:

  • Step1: First, find the product of π and the radius (r) of the semicircle.
  • Step 2: Next, find the diameter of the semicircle.
  • Step 3: Then Add the values obtained in the above two steps.
  • Step 4: Thus the value obtained is the perimeter of the semicircle.

2. What is the difference between circumference and Perimeter of Semicircle?

The perimeter of a semicircle and the circumference of a semicircle mean the same. Both are referred to the total length of the boundary of a semicircle. Therefore, the circumference of a semicircle is another name for the perimeter of a semicircle.

3. Is a semicircle is half the circle?

Yes, a semicircle is half the circle. It means a circle can be divided into two semicircles.

4. What is the shape of a semicircle? 

The shape of a semicircle is obtained by cutting a circle into two equal parts along its diameter and the full arc of a semicircle is always measured 180 degrees. An example of a semicircle shape is a protractor.

5. What is the angle of the semicircle? 

The angle of the semicircle is 90 degrees, the angle is made by the triangle in a semicircle is a right angle.

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