The Area of a Square in Terms of Its Diagonal $z$

Multiple Choice

The area of a square in terms of its diagonal $z$ is given by the formula $A=\frac{1}{2} z^{2}$ . Use a differential to estimate the change in the area of a square whose diagonal has been increased from $6.0 \mathrm{~cm}$ to 6.2 $\mathrm{cm}$ .

A) $\mathrm{dA}=1.2 \mathrm{~cm}^{2}$
B) $\mathrm{dA}=1.8 \mathrm{~cm}^{2}$
C) $\mathrm{dA}=0.4 \mathrm{~cm}^{2}$
D) $\mathrm{dA}=0.2 \mathrm{~cm}^{2}$