Question

Suppose that a circular coin has an area a, a radius of r, and a diameter of
d. write a as a function of
d.

Answer 1

The area of a circle is A= pi * r^2
The radius is half of the diameter, r = (1/2)d
Replace r in the formula with the expression with d

A  = pi * ((1/2)d)^2

A = pi * 1/4 * d^2

A = (pi * d^2)/4