I am so confuse about this question
Determine the area of a circular enclosure and a square enclosure made with 107 meters of fence.
To determine the area of both the circular enclosure and the square enclosure, we need to use some basic formulas.
1. Circular Enclosure:
Let's assume the radius of the circular enclosure is 'r'. The circumference of a circle can be calculated using the formula C = 2πr, where π is approximately 3.14.
In this case, the circumference of the circular enclosure is equal to the total length of the fence, which is 107 meters:
C = 107 meters.
We can rearrange the formula to solve for 'r':
2πr = C
r = C / (2π)
r = 107 meters / (2 * 3.14)
r ≈ 17.07 meters (rounded to two decimal places).
The area of a circle can be calculated using the formula A = πr^2. Let's plug in the value of 'r' we just found:
A = π * (17.07 meters)^2
A ≈ 914.08 square meters (rounded to two decimal places).
Therefore, the area of the circular enclosure is approximately 914.08 square meters.
2. Square Enclosure:
Let's assume the side length of the square enclosure is 's'.
The perimeter of a square is given by the formula P = 4s. In this case, the perimeter of the square enclosure is equal to the total length of the fence, which is 107 meters:
P = 107 meters.
We can rearrange the formula to solve for 's':
4s = P
s = P / 4
s = 107 meters / 4
s = 26.75 meters.
The area of a square can be calculated using the formula A = s^2. Let's substitute the value of 's':
A = (26.75 meters)^2
A ≈ 716.56 square meters (rounded to two decimal places).
Therefore, the area of the square enclosure is approximately 716.56 square meters.
To determine the area of the circular enclosure and the square enclosure made with 107 meters of fence, we can use basic geometry concepts.
First, let's start with the circular enclosure:
The perimeter of a circle is given by the formula: P = 2πr, where P is the perimeter and r is the radius. In this case, the perimeter is given as 107 meters.
Using the formula, we can rearrange it to solve for the radius:
r = P / (2π) = 107 / (2π) ≈ 17.03 meters
The area of a circle is given by the formula: A = πr^2, where A is the area and r is the radius.
Substituting the value of the radius (17.03 meters):
A = π(17.03)^2 ≈ 910.29 square meters
So, the area of the circular enclosure is approximately 910.29 square meters.
Now, let's move on to the square enclosure:
The perimeter of a square is given by the formula: P = 4s, where P is the perimeter and s is the length of one side. In this case, the perimeter is given as 107 meters.
Using the formula, we can rearrange it to solve for the length of one side:
s = P / 4 = 107 / 4 = 26.75 meters
The area of a square is given by the formula: A = s^2, where A is the area and s is the length of one side.
Substituting the value of the side length (26.75 meters):
A = (26.75)^2 ≈ 716.56 square meters
So, the area of the square enclosure is approximately 716.56 square meters.
To summarize:
- The area of the circular enclosure is approximately 910.29 square meters.
- The area of the square enclosure is approximately 716.56 square meters.