Last updated on August 1st, 2025
A semicircle is half of a circle, and its properties and formulas are a fundamental part of geometry. In this topic, we will learn the formulas related to the perimeter, area, and other characteristics of a semicircle.
Understanding the properties of a semicircle involves using specific formulas for its perimeter, area, and other measurements. Let’s learn these formulas.
The perimeter of a semicircle includes its curved edge and the diameter. It is calculated using the formula:
Perimeter of a semicircle = πr + 2r, where r is the radius of the semicircle.
The area of a semicircle is half of the area of a full circle. It is calculated using the formula:
Area of a semicircle = (πr²)/2, where r is the radius.
The diameter of a semicircle is twice the radius.
Diameter = 2r, where r is the radius of the semicircle.
In geometry and real-life applications, semicircle formulas help analyze and understand the properties of semicircular objects. Here are some important aspects of semicircle formulas:
Students often find geometry challenging, but there are ways to master semicircle formulas:
Students often make errors when calculating values related to semicircles. Here are some mistakes and ways to avoid them:
Find the perimeter of a semicircle with a radius of 7 cm.
The perimeter is approximately 36.98 cm.
Perimeter = πr + 2r
= (3.14 × 7) + (2 × 7)
= 21.98 + 14
= 35.98 cm (rounded to 36.98 cm).
Calculate the area of a semicircle with a radius of 4 m.
The area is approximately 25.12 m².
Area = (πr²)/2
= (3.14 × 4²)/2
= (3.14 × 16)/2
= 25.12 m².
What is the diameter of a semicircle with a radius of 5 mm?
The diameter is 10 mm.
Diameter = 2r
= 2 × 5 = 10 mm.
Find the perimeter of a semicircle with a radius of 3.5 inches.
The perimeter is approximately 19.99 inches.
Perimeter = πr + 2r
= (3.14 × 3.5) + (2 × 3.5)
= 10.99 + 7 = 17.99 inches (rounded to 19.99 inches).
Calculate the area of a semicircle with a radius of 10 cm.
The area is approximately 157 cm².
Area = (πr²)/2
= (3.14 × 10²)/2
= (3.14 × 100)/2
= 157 cm².
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