A certain two dimensional shape has the following integrals

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dA=9in{?}^{(}()()2)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$xdA$=27in{?}^{(}()()3)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$ydA$=18in{?}^{(}()()3)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}dA=85\mathrm{.}5in{?}^{(}()()4)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$xydA$=49\mathrm{.}5in{?}^{(}()()4)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{y}^{2}dA=54in{?}^{(}()()4)$

where $dA$ is a differential area element, $d{x}^{*}dy.$

Find the following properties of the shape

Centroid $=(\stackrel{}{x}\frac{,}{b}ar(Y))=(,)in.$

The Area Moments of Intertia about axes parallel

to the $x$ and $y$ axes through the centroid.

$I_{x^{\text{'}}}=in{?}^{(}()()4)$

$I^{\text{'}}=in{?}^{(}()()4)$

Product of Inertia, $I_{x^{\text{'}}{y}^{\text{'}}}=,$ in ${?}^4$

Polar Moment of Inertia, $J(x^{\text{'}},y^{\text{'}})=$ in ${?}^4$