Question

If the perimeter of a semicircle park is 72 meters, find the area and radius.

Area: 81 square meters, Radius: 9 meters
Area: 72 square meters, Radius: 6 meters
Area: 54 square meters, Radius: 4.5 meters
Area: 64 square meters, Radius: 8 meters

Answer 1

The radius of the semicircle park with a perimeter of 72 meters is approximately 9 meters, and the area is approximately 81 square meters. To solve this, we use the perimeter of a semicircle formula and then calculate the area by plugging in the radius value.

Step-by-step explanation:

To calculate the perimeter and area of a semicircle with a given perimeter of 72 meters, it is necessary to use the formula for the perimeter of a semicircle, which is P = πr + 2r, where π is approximately 3.14159 and r is the radius. Given that the perimeter is 72 meters, we can solve for the radius using this equation. Once the radius is found, we can then use the formula for the area of a semicircle, A = (πr²)/2, to find the area.

First, let's calculate the radius from the given perimeter:

1. Set up the equation 72 = πr + 2r.
2. Combine terms: 72 = r(π + 2).
3. Divide both sides by (π + 2) to solve for r: r = 72 / (π + 2).
4. Using a calculator, we find the radius is approximately 9 meters.

Now, use the radius to calculate the area:

1. Plug in the radius into the area formula: A = (π(9²))/2.
2. Calculate the area using a calculator: A is approximately 81 square meters.

Therefore, the radius of the semicircle park is approximately 9 meters and the area is approximately 81 square meters.