The side of an equivalent square field of a circular field with diameter D is approximately given by which of the following?

To determine the side length of an equivalent square field that has the same area as a circular field with diameter D, it's essential to first calculate the area of the circular field. The area A of a circle is given by the formula:

A = π * (radius)².

Since the radius R is half the diameter D, we can express the radius as R = D/2. Thus, the area becomes:

A = π * (D/2)² = π * D² / 4.

Now, for an equivalent square field, where the side length S needs to be found, the area of the square is given by:

Area of square = S².

To find the side length of the square that matches the area of the circle, we set these two areas equal:

S² = π * D² / 4.

To solve for S, we take the square root of both sides:

S = √(π * D² / 4) = (D / 2) * √π.

Now, the value of √π is approximately 1.772. Therefore, we can rewrite the side length S:

S ≈ (D / 2) * 1.772 = 0.