What is the area formula for a circle if expressing in terms of diameter?

The area formula for a circle can indeed be expressed in terms of diameter. The standard formula for the area of a circle in terms of the radius (r) is πr². Since the diameter (d) is twice the radius (d = 2r), you can express the radius in terms of the diameter by rearranging it to r = d/2.

Substituting this back into the area formula gives:

Area = π(d/2)²
= π(d²/4)
= π(d²)/4.

This shows that option B, π(d²)/4, correctly represents the area of a circle expressed in terms of its diameter. Understanding this relationship between diameter and radius is essential in geometry and helps reinforce the connections between different properties of circles.