Answer:
[tex]A=\pi \frac{d^2}{4}[/tex]
Step-by-step explanation:
The typical equation for the area of a circle is [tex]A=\pi r^2[/tex]. Since the answer choices are in terms of d, the diameter of the circle, you will need to find r in terms of d.
To find r in terms of d, you know that the diameter of a circle is two times its radius. As an equation, this is
[tex]d=2r[/tex], or solving for r,
[tex]r = \frac{d}{2}[/tex].
Now that you have an equation for r in terms of d, you can substitute r with [tex]\frac{d}{2}[/tex] from the original equation.
[tex]A=\pi r^2[/tex]
[tex]A=\pi (\frac{d}{2})^2[/tex]
[tex]A=\pi \frac{d^2}{4}[/tex]
