What is the formula for area when you know the diameter?

To calculate the area of a circle when you know the diameter, you can use the formula ( A = \pi r^2 ), where ( r ) is the radius. Since the radius is half of the diameter, you can express the radius as ( r = \frac{d}{2} ), where ( d ) is the diameter. Substituting this into the area formula gives ( A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} ). Thus, the area can be calculated using the formula ( A = \frac{\pi d^2}{4} ).