What Is a Semicircle?
A semicircle is a two-dimensional geometric shape that is formed by dividing a circle into two equal parts, where one part is a half-circle. The boundary of a semicircle consists of an arc and a diameter that connects the endpoints of the arc. The diameter of a semicircle is twice the length of its radius.
The word “semi” means half, so a semicircle is literally half of a circle. It has rotational symmetry of 180 degrees, which means that it looks the same when rotated by 180 degrees around its center.
Area of a Semicircle
The area of a semicircle is half of the area of the corresponding full circle.
If r is the radius of the semicircle, then
Area of circle = πr²,
where π (pi) is a mathematical constant approximately equal to 3.14159.
So, the area of the semicircle is:
½ * πr²
or
Area of semicircle = πr² / 2
Therefore, the area of a semicircle is equal to half the area of a circle.
How to Find the Area of a Semicircle
To find the area of a semicircle, you can use the following formula:
Area of a semicircle = (π * r²)/2
Where r is the radius of the semicircle, and π (pi) is a mathematical constant approximately equal to 3.14159.
Steps to find the area of a semicircle:
Step1. Measure the radius of the semicircle. The radius is the distance from the center of the circle to the edge of the semicircle.
Step 2. Square the radius. Multiply the radius by itself.
Step 3. Multiply the squared radius by pi. Use the value of pi as 3.14159.
Step 4. Divide the result by 2 to get the area of the semicircle.
For example, let’s say the radius of the semicircle is 5 cm. To find the area of the semicircle, we can use the formula:
Area of a semicircle = (π * r²)/2
= (3.14159 * 5²)/2
= (3.14159 * 25)/2
= 39.27 cm²
Therefore, the area of the semicircle is 39.27 square centimeters.
Area of Semicircle Formula
The formula for the area of a semicircle is:
where:
A = area of the semicircle
r = radius of the semicircle
π ≈ 3.14159 (pi, a mathematical constant representing the ratio of the circumference of a circle to its diameter)