Last updated on August 5th, 2025
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.
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.
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.
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.
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.
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.
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.
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.
Perimeter = 20.56 cm
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.
Area = 76.93 cm²
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.
Perimeter = 28.84 cm
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.
Radius = 4 cm
Students often make errors when calculating the surface area of a semicircle. Here are some common mistakes and tips to avoid them.
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.
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