P$1)$ Given: A $2$D rectangular plate ABCD deforms to $A^{\text{'}}{B}^{\text{'}}{C}^{\text{'}}D$ as shown while all edges remain straight. $C^{\text{'}}$ is on the $x-$axis. Average normal strains along $x$ and $y$ axes at $D$ are ${}_x=0\mathrm{.}004$ and ${}_y=0\mathrm{.}005$ respectively, and the average shear strain ${}_{xy}$ at $D$ is $0\mathrm{.}02$ radians.

Find:

$($a$)$ The average normal strain along diagonal $AC$

$($b$)$ The average shear strain ${}_{xy}$ at $B$

Figure: