Mathematics - Area Under Curves Question with Solution | TestHub

Let $S=\{(x,y)\in \mathbb{R}\times \mathbb{R}:x\ge 0,y\ge 0,y^2\le 4x,y^2\le 12-2x$ and $3y+\sqrt{8}x\le 5\sqrt{8}\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal to