Correct. The quarter has a diameter of about 24 millimeters. Its radius is half of this. So substitute $\displaystyle{r}={12}\usepackage{cmbright}\Huge\$ in the formula $\displaystyle{A}=\pi{{r}}^{{2}}\usepackage{cmbright}\Huge\$ to find the area of one side.

$\displaystyle{A}=\pi{{\left({12}\right)}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle{A}=\pi\cdot{144}\usepackage{cmbright}\Huge\$

$\displaystyle{A}\approx{3.14}\cdot{144}={452.16}\approx{452}\usepackage{cmbright}\Huge\$ square millimeters

The area of one side of a U.S. quarter is approximately 452 square millimeters.