Circle Area A71255

1. **State the problem:** We need to express the area $A$ of a circle in terms of its diameter $d$. 2. **Recall the formula for the area of a circle:** The area is usually given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Relate diameter to radius:** The diameter $d$ is twice the radius, so $$d = 2r \implies r = \frac{d}{2}$$. 4. **Substitute radius in the area formula:** $$A = \pi \left(\frac{d}{2}\right)^2 = \pi \frac{d^2}{4} = \frac{\pi}{4} d^2$$ 5. **Interpretation:** The area equals the product of the square of the diameter and the constant $\frac{\pi}{4}$. **Final equation:** $$A = \frac{\pi}{4} d^2$$