Suppose the radius of a circle is \color{R_COLOR}{R}. What is its area?
Suppose the diameter of a circle is \color{D_COLOR}{2 * R}. What is its area?
First, find the radius:
\begin{align}
r &= \dfrac d2 \\
r &= \dfrac{\color{D_COLOR}{2 * R}}{2} \\
r &= \color{R_COLOR}{R}
\end{align}
Suppose the circumference of a circle is \color{C_COLOR}{2 * R\pi}. What is its area?
First, find the radius:
\begin{align}
r &= \dfrac{c}{2\pi} \\
r &= \dfrac{\color{C_COLOR}{2 * R\pi}}{2} \\
r &= \color{R_COLOR}{R}
\end{align}
The equation for the area of a circle is:
K = \pi r^2
K = \pi \cdot \color{R_COLOR}{R}^2
K = \color{K_COLOR}{R * R\pi}