Perimeter of a Semi-Circular Park

To find the area or radius of a semi-circular park, we first need to understand the concept of perimeter and how it relates to a semi-circle.

Perimeter:
Perimeter is the total distance around the outside of a shape. It is the sum of all the lengths of its sides or edges. The unit of measurement for perimeter is usually the same as the unit used to measure the sides or edges.

Semi-Circular Park:
A semi-circle is half of a circle. It is formed by taking a diameter of a circle and bending it to create an arc. In the case of a semi-circular park, the perimeter will be the sum of the curved part (the arc) and the straight part (the diameter).

Calculating Perimeter:
To find the perimeter of a semi-circular park, we need to know the length of the arc and the diameter of the park.

Step 1: Finding the length of the arc:
The length of the arc of a semi-circle can be calculated using the formula:
Arc Length = π * Diameter / 2
In this case, we are given the perimeter of the park, which is 72m. Since the perimeter of a semi-circle is the sum of the arc and the diameter, we can set up the equation:
Arc Length + Diameter = 72m

Step 2: Finding the diameter:
Since we know the length of the arc can be calculated using the formula π * Diameter / 2, we can rearrange the equation to solve for the diameter:
Diameter = 2 * (Perimeter - Arc Length) / π

Step 3: Finding the radius:
The radius of a semi-circle is half the length of the diameter. We can calculate the radius using the formula:
Radius = Diameter / 2

Step 4: Finding the area:
Once we have the radius, we can calculate the area of the semi-circular park using the formula:
Area = π * Radius^2

Conclusion:
To find the area or radius of a semi-circular park with a perimeter of 72m, we need to follow the steps mentioned above. By using the formulas for calculating the length of the arc, diameter, radius, and area, we can determine the required values.