Area of Semicircle Calculator
Enter the radius of the semicircle:
The area of a semicircle is a common concept in geometry and can be useful in various calculations involving circular objects. A semicircle is half of a circle and can be obtained by cutting a circle along its diameter. The formula for finding the area of a semicircle is closely related to the formula for the area of a circle.
Formula for the Area of a Semicircle:
The formula for the area of a circle is A = πr^2, where A is the area of the circle and r is the radius of the circle. Since a semicircle is half of a circle, the formula for the area of a semicircle is:
A = 1/2πr^2
where A is the area of the semicircle and r is the radius of the semicircle.
Example Problems:
- Find the area of a semicircle with a radius of 4 cm.
Solution:
Using the formula, A = 1/2πr^2, where r = 4 cm:
A = 1/2π(4)^2 A = 8π A ≈ 25.12 cm^2
Therefore, the area of the semicircle is approximately 25.12 cm^2.
- A semicircular window has a diameter of 6 feet. What is the area of the window?
Solution:
The radius of the window is half of the diameter, or 3 feet. Using the formula, A = 1/2πr^2, where r = 3 feet:
A = 1/2π(3)^2 A = 9π/2 A ≈ 14.14 ft^2
Therefore, the area of the semicircular window is approximately 14.14 square feet.
- A semicircular garden bed has a radius of 8 meters. What is the area of the garden bed?
Solution:
Using the formula, A = 1/2πr^2, where r = 8 meters:
A = 1/2π(8)^2 A = 32π A ≈ 100.53 m^2
Therefore, the area of the semicircular garden bed is approximately 100.53 square meters.
- A semicircular pool has a diameter of 10 feet. What is the area of the pool?
Solution:
The radius of the pool is half of the diameter, or 5 feet. Using the formula, A = 1/2πr^2, where r = 5 feet:
A = 1/2π(5)^2 A = 25π/2 A ≈ 39.27 ft^2
Therefore, the area of the semicircular pool is approximately 39.27 square feet.
In summary, the area of a semicircle can be calculated using the formula (πr^2)/2, where π is the mathematical constant pi and r is the radius of the circle. The formula for the area of a full circle, πr^2, is divided by 2 to obtain the area of a semicircle.
