A semicircle is simply half of a circle.
This article breaks down how to calculate the area of a semicircle, including different methods you can use, and offers a handy area of semicircle calculator.
Semicircles are everywhere, from architecture to design, so understanding how to work with them is useful in many real-world situations.
Understanding the Semicircle
When you cut a circle in half through its center (or diameter), you get a semicircle.
Here are the important measurements you’ll need to know about a semicircle:
- Radius: The distance from the center of the semicircle to any point on the curved line.
- Diameter: The distance across the semicircle, passing through the center. (The diameter is twice the length of the radius.)
- Arc: The curved line that forms half the circle.
You see semicircles all around you every day, in mirrors, tables, sofas, windows, protractors, and even pizza slices!
Calculating the Area of a Semicircle
A semicircle is simply half of a circle. So, not surprisingly, the area of a semicircle is half the area of a full circle.
The General Formula
The formula for the area of a semicircle is:
Area = (π r2) / 2
where π (pi) is roughly 3.14159 and r is the radius of the semicircle.
Method 1: Using the Radius
To calculate the area if you know the radius, follow these steps:
- Square the radius.
- Multiply the result by π.
- Divide by 2.
For example, let’s say you have a semicircle with a radius of 5 inches. Then,
Area = (3.14159 52) / 2 = approximately 39.27 square inches.
Method 2: Using the Diameter
If you know the diameter, you can find the radius by dividing the diameter by 2:
Radius = Diameter / 2
Then, the formula for the area using the diameter is:
Area = (π (d/2)2) / 2 where d is the diameter
For example, let’s say you have a semicircle with a diameter of 10 inches. Then, the radius is 10 / 2 = 5 inches. And the area is:
Area = (3.14159 52) / 2 = approximately 39.27 square inches.
Calculating area from circumference
Believe it or not, you can calculate the area of a semicircle if you only know its circumference.
Relationship between circumference and radius
You probably remember that the circumference of a circle is 2 π r.
In a semicircle, r = C / π, where C is the length of the curved part of the semicircle. Keep in mind that the full perimeter of a semicircle includes the diameter, which is twice the radius.
Formula for area using circumference
That means the formula for a semicircle’s area is (π (C/π)2) / 2.
Example calculation
For example, let’s say you have a semicircle with a curved part of the circumference measuring 10 inches.
That would mean the radius = 10 / 3.14159, or about 3.183 inches.
The area would then be (3.14159 (3.183)2) / 2 = roughly 15.92 square inches.
How to calculate the perimeter of a semicircle
It’s important to remember that a semicircle’s circumference is not the same as its perimeter. The circumference only refers to the curved part. The perimeter is the curved part plus the diameter (the straight line across).
Here’s how to find the perimeter:
Perimeter = (π r) + 2r
So, for example, if you have a semicircle with a radius of 5 inches, the perimeter would be approximately (3.14159 5) + (2 5) = 25.71 inches.
Conclusion
Whether you know the radius, diameter, or circumference, calculating the area of a semicircle is simple. Knowing these formulas makes it easy to calculate the area of a semicircle in many real-world situations.