102 LearnersLast updated on August 5th, 2025
Surface Area of Semicircle
A semicircle is a two-dimensional shape that represents half of a circle. The surface area of a semicircle refers to the total area covered by its boundary. The surface area of a semicircle includes the curved arc and the straight diameter line. In this article, we will learn about the surface area of a semicircle.
What is the Surface Area of a Semicircle?
The surface area of a semicircle is the total area occupied by the boundary or surface of a semicircle. It is measured in square units.
A semicircle is created by dividing a circle into two equal halves. It has a curved boundary called the arc and a straight boundary called the diameter. The surface area of a semicircle includes the area of the curved arc and the straight line.
Surface Area of a Semicircle Formula
A semicircle has a curved arc and a straight diameter line. Its surface area is calculated by considering both the area of the semicircle and the area of the bounding diameter line:
Area of a semicircle = (1/2) × πr² Where r is the radius of the semicircle.
Area of the Semicircle
The area of the semicircle is half the area of a full circle. Since a full circle has an area of πr², the area of a semicircle is given by:
Area of the semicircle = (1/2) × πr² square units Here, r is the radius of the semicircle.
Perimeter of a Semicircle
The perimeter of a semicircle includes the length of the curved arc plus the diameter of the semicircle. The formula for the perimeter is:
Perimeter of a semicircle = πr + 2r Where r is the radius of the semicircle.
Common Mistakes and How to Avoid Them in the Surface Area of a Semicircle
Students often make mistakes while calculating the surface area of a semicircle, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
Confusion between Area and Perimeter
Students sometimes confuse the formulas for area and perimeter. Always remember that the area measures the space inside the semicircle, while the perimeter measures the length around it.
Mistake 1
Forgetting the Diameter in the Perimeter
Some students forget to add the diameter when calculating the perimeter. Remember that the perimeter of a semicircle includes both the curved arc and the diameter.
Mistake 2
Using the Wrong Value for π
A frequent mistake is using an incorrect value for π. Use 3.14 or 22/7 for better accuracy.
Mistake 3
Misunderstanding the Concept of Semicircle
Some students mistakenly calculate the area as if it were a full circle. Remember, a semicircle is half of a circle, so the area is half of πr².
Mistake 4
Assuming Semicircle Area and Circle Area are the Same
Some students wrongly assume that the area of a semicircle is the same as a circle. It's crucial to remember that a semicircle is only half of a circle.
Mistake 5
Solved Examples of Surface Area of Semicircle
Find the area of a semicircle with a radius of 5 cm.
Area = 39.25 cm²
Problem 1
Given r = 5 cm. Use the formula: Area = (1/2) × πr² = (1/2) × 3.14 × 5² = (1/2) × 3.14 × 25 = 39.25 cm²
Find the perimeter of a semicircle with a radius of 4 cm.
Explanation
Perimeter = 20.56 cm
Problem 2
Use the formula: Perimeter = πr + 2r = 3.14 × 4 + 2 × 4 = 12.56 + 8 = 20.56 cm
A semicircle has a radius of 7 cm. Find its area.
Explanation
Area = 76.93 cm²
Problem 3
Use the formula: Area = (1/2) × πr² = (1/2) × 3.14 × 7² = (1/2) × 3.14 × 49 = 76.93 cm²
Calculate the perimeter of a semicircle with a radius of 6 cm.
Explanation
Perimeter = 28.84 cm
Problem 4
Perimeter = πr + 2r = 3.14 × 6 + 2 × 6 = 18.84 + 12 = 28.84 cm
Find the radius of a semicircle if its area is 50.24 cm².
Explanation
Radius = 4 cm
It is the total area that covers the inside of a semicircle, calculated as half the area of a full circle.
1.What is included in the perimeter of a semicircle?
2.How is a semicircle different from a full circle?
3.What is the formula for the area of a semicircle?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Semicircle
Students often make errors when calculating the surface area of a semicircle. Here are some common mistakes and tips to avoid them.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
