Answer
No. This is because the fraction is in an improper form.
Work Step by Step
$3\frac{1}{2}=\frac{7}{2}$
Thus, $(3\frac{1}{2})^{2} = (\frac{7}{2})^{2} = \frac{49}{4}$ Which is not equal to $\frac{37}{4}$ or $9\frac{1}{4}$.
Therefore, It is not true because the fraction is in an improper form.