A farmer had a fence that encloses a square plot with an area of 36 meters squared. If the garnet uses this fence to enclose a circular flower garden, what will the area of the garden be?
the square is 6x6, so the perimeter = 4*6 = 24
for the circle, area = pi * r^2 = pi * (24/2pi)^2 = 144/pi = 45.84 m^2
To find the area of the circular flower garden, we need to determine the radius of the circle. Since the fence encloses a square plot with an area of 36 square meters, we can find the length of one side of the square by taking the square root of 36.
√36 = 6 meters
Since the plot is square, all four sides are equal. Therefore, the perimeter of the square is 4 times the length of one side.
Perimeter = 4 * 6 = 24 meters
The perimeter of the square fence will be equal to the circumference of the circular garden. The formula for the circumference of a circle is:
Circumference = 2πr
To find the radius of the circular garden, we divide the circumference by 2π.
24 = 2πr
Dividing both sides of the equation by 2π, we can solve for r.
r = 24 / (2π)
r ≈ 3.82 meters
Now we can use the formula for the area of a circle to find the area of the garden.
Area = πr^2
Substituting the value of r,
Area = π(3.82)^2
Area ≈ 45.85 square meters
Therefore, the area of the circular flower garden will be approximately 45.85 square meters.
To find the area of the circular flower garden, we need to know the radius of the circle formed by the fence.
Since the plot is square and has an area of 36 square meters, we can find the length of one side of the square plot by taking the square root of the area:
Side length = √(Area of square plot) = √36 = 6 meters
In a square plot, the diagonal is equal to the diameter of the circle that can be inscribed in it. Drawing a diagonal from one corner to another across the square divides the square into two equal right triangles. The hypotenuse of one of these triangles is the side length of the square, and the other two sides are equal.
Using the Pythagorean theorem, we can find the diagonal (D) of the square plot:
D^2 = (Side length)^2 + (Side length)^2
D^2 = 6^2 + 6^2
D^2 = 72
D ≈ 8.49 meters
Now that we know the diameter of the circle, we can find the radius (r) by dividing the diameter by 2:
r = D/2 ≈ 8.49/2 ≈ 4.24 meters
Finally, we can calculate the area of the circular flower garden using the formula for the area of a circle:
Area of garden = π * r^2
Area of garden ≈ 3.14 * 4.24^2
Area of garden ≈ 56.56 square meters
Therefore, the area of the circular flower garden will be approximately 56.56 square meters.