$5.20$ points$$A $4-$node isoparametric element is shown below. Assume the thickness of the element is $t=0\mathrm{.}5.$

Compute the Jacobian matrix $[$J$]$ and its determinant $|J|$ at the centroid of the element.

Compute the strains ${}_x,{}_y,{}_{xy}$ at the centroid of the element if the nodal displacements are $,-1,2,2,2,-1$