Final answer:
To find the area of a semicircle with a 24-inch diameter, divide the diameter by 2 to get the radius, calculate the full circle's area, and then divide by 2. The final area of the semicircle is 226.19 square inches when rounded to the nearest hundredth.
Step-by-step explanation:
The area of a semicircle with a diameter of 24 inches can be found using the area formula for a circle, A = πr^2, and then taking half of that area because a semicircle is half of a circle. First, we find the radius by dividing the diameter by 2, which gives us 12 inches. Then we calculate the area of the full circle using the radius and finally divide it by 2 to get the area of the semicircle.
- Find the radius (r): Diameter (D) / 2 = 24 inches / 2 = 12 inches.
- Calculate the area of the full circle: A = πr^2 = π * (12 inches)^2.
- Divide by 2 to get the semicircle area: Area of semicircle = A / 2.
Using π as 3.14159, the calculations would look like this:
- A = π * (12 inches)^2 = 3.14159 * 144 square inches = 452.389 square inches.
- Area of semicircle = 452.389 square inches / 2 = 226.1945 square inches.
Rounded to the nearest hundredth, the area of the semicircle is 226.19 square inches.