A certain two dimensional shape has the following integrals

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dA=18in{?}^{(}()()2)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$xdA$=54in{?}^{(}()()3)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$ydA$=54in{?}^{(}()()3)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}dA=198in{?}^{(}()()4)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$xydA$=144in{?}^{(}()()4)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{y}^{2}dA=198in{?}^{(}()()4)$

where $dAis$ 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.

$I_{x^{\text{'}}}=in4$

$I_{y^{\text{'}}}=in4$

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

Polar Moment $of$ Inertia, $J_{(x^{\text{'}},y^{\text{'}})}=,in4$