Area of Semicircle
2026-02-28 11:12 Diff
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Last updated on September 13, 2025

Area is the space inside the boundaries of a two-dimensional shape or surface. There are different formulas for finding the area of various shapes/figures. These are widely used in architecture and design. In this section, we will find the area of the semicircle.

What is the Area of Semicircle?

A semicircle is a two-dimensional shape that forms half of a circle. The area of the semicircle is the total space it encloses. Understanding the properties of a circle helps in calculating the area of a semicircle.

Area of the Semicircle Formula

To find the area of the semicircle, we use the formula: \( \frac{\pi r^2}{2} \), where \( r \) is the radius of the circle from which the semicircle is formed. Now let’s see how the formula is derived.

Derivation of the formula:- The area of a full circle is \(\pi r^2\). Since a semicircle is half of a circle, its area is half of the full circle's area. Therefore, the area of the semicircle = \(\frac{\pi r^2}{2}\).

How to Find the Area of Semicircle?

We can find the area of the semicircle using the radius of the circle. The formula is straightforward since a semicircle is simply half of a circle. Let’s discuss how to use the formula:

If the radius \( r \) is given, we find the area of the semicircle using the formula: Area = \(\frac{\pi r^2}{2}\). For example, if the radius is 10 cm, what will be the area of the semicircle? Area = \(\frac{\pi ×10^2}{2}\) = \(\frac{\pi × 100}{2}\) = \(50\pi \approx 157.08\) The area of the semicircle is approximately 157.08 cm\(^2\).

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Unit of Area of Semicircle

We measure the area of a semicircle in square units. The measurement depends on the system used: In the metric system, the area is measured in square meters (m\(^2\)), square centimeters (cm\(^2\)), and square millimeters (mm\(^2\)).

In the imperial system, the area is measured in square inches (in\(^2\)), square feet (ft\(^2\)), and square yards (yd\(^2\)).

Special Cases or Variations for the Area of Semicircle

The area of a semicircle is straightforward to calculate once the radius of the circle is known. Take a look at the special cases:

Case 1: Using the radius If the radius is given, use the formula Area = \(\frac{\pi r^2}{2}\), where \( r \) is the radius.

Case 2: Using the diameter If the diameter is given, first find the radius by dividing the diameter by 2, and then use the formula Area = \(\frac{\pi r^2}{2}\).

Tips and Tricks for Area of Semicircle

To ensure correct results while calculating the area of the semicircle, here are some tips and tricks you should know about:

  • Always ensure that the radius is correctly measured or calculated from the diameter.
     
  • Use \(\pi\) as 3.14159 or a more precise value for more accurate results.
     
  • Remember that the area of the semicircle is always half of the area of the full circle with the same radius.

Common Mistakes and How to Avoid Them in Area of Semicircle

It is common for students to make mistakes while finding the area of the semicircle. Let’s take a look at some mistakes made by students.

Problem 1

A semicircular window has a radius of 7 m. What will be the area?

Okay, lets begin

We will find the area as approximately 76.97 m\(^2\).

Explanation

Here, the radius \( r \) is 7 m.

The area of the semicircle = \(\frac{\pi  × 7^2}{2}\) = \(\frac{\pi  × 49}{2}\) = \(24.5\pi \approx 76.97\) m\(^2\).

Well explained 👍

Problem 2

What will be the area of the semicircle if the diameter is 16 cm?

Okay, lets begin

We will find the area as approximately 100.53 cm\(^2\).

Explanation

If the diameter is given, first find the radius by dividing the diameter by 2.

Here, the diameter is 16 cm, so the radius is 8 cm.

The area of the semicircle = \(\frac{\pi × 8^2}{2}\) = \(\frac{\pi × 64}{2}\) = \(32\pi \approx 100.53\) cm\(^2\).

Well explained 👍

Problem 3

The area of a semicircular garden path is 157 m\(^2\). What is the radius?

Okay, lets begin

We find the radius as approximately 10 m.

Explanation

To find the radius, use the formula \( \frac{\pi r^2}{2} = 157 \).

Rearrange to find \( r \): \(\pi r^2 = 314\) \(r^2 = \frac{314}{\pi}\) \(r \approx \sqrt{\frac{314}{3.14159}} \approx 10\) m.

Well explained 👍

Problem 4

Find the area of the semicircle if its radius is 12 cm.

Okay, lets begin

We will find the area as approximately 226.2 cm\(^2\).

Explanation

The given radius is 12 cm.

The area of the semicircle = \(\frac{\pi × 12^2}{2}\) = \(\frac{\pi × 144}{2}\) = \(72\pi \approx 226.2\) cm\(^2\).

Well explained 👍

Problem 5

Help Lisa find the area of the semicircle if the diameter is 20 m.

Okay, lets begin

We will find the area as approximately 157 m\(^2\).

Explanation

The diameter is 20 m, so the radius is 10 m.

The area of the semicircle = \(\frac{\pi × 10^2}{2}\) = \(\frac{\pi × 100}{2}\) = \(50\pi \approx 157\) m\(^2\).

Well explained 👍

FAQs on Area of Semicircle

1.Is it possible for the area of the semicircle to be negative?

No, the area of the semicircle can never be negative. The area of any shape will always be positive.

2.How to find the area of a semicircle if the diameter is given?

If the diameter is given, first calculate the radius by dividing the diameter by 2, then use the formula: area = \(\frac{\pi r^2}{2}\).

3.How to find the area of the semicircle if only the circumference is given?

If the circumference is given, calculate the radius using the formula \( C = \pi d \) (where \( d \) is the diameter), and then find the area using the formula: area = \(\frac{\pi r^2}{2}\).

4.How is the perimeter of the semicircle calculated?

The perimeter of a semicircle is calculated using the formula \( P = \pi r + 2r \), where \( r \) is the radius.

5.What is meant by the area of the semicircle?

The area of the semicircle is the total space occupied by the semicircle.

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