Consider a badminton racket with length scales as shown in the...

${I}_{A} = \left[\dfrac{M{r}^{2}}{2} + M{\left(7r - \dfrac{r}{2}\right)}^{2}\right] + \left[\dfrac{M ( 6r{)}^{2}}{12} + \left(M{\left(3r - \dfrac{r}{2}\right)}^{2}\right)\right]$

$= \left\{\dfrac{M{r}^{2}}{2} + M\dfrac{( 169 ) {r}^{2}}{4}\right\} + \left\{3M{r}^{2} + \dfrac{25M{r}^{2}}{4}\right\} = \dfrac{171M{r}^{2}}{4} + \dfrac{37M{r}^{2}}{4} = \dfrac{208}{4}M{r}^{2} = 52M{r}^{2}$