The area of the region ( x , y ) : 0 ≤ x ≤ 9 4 ,    0 ≤ y ≤ 1 , &#160…

The region is a quadrilateral $ABCD$

Now, area of the quadrilateral $ABCD=$area of triangle $ABD+$area of the triangle $BCD$ 

So, area $=\frac{1}{2}\left|\begin{array}{ccc}\frac{3}{2}& \frac{1}{2}& 1\\ 2& 0& 1\\ \frac{9}{4}& \frac{3}{4}& 1\end{array}\right|+\frac{1}{2}\times \left(\frac{9}{4}-2\right)\times \frac{3}{4}$

$=\frac{1}{2}\left\{-2\left(\frac{1}{2}-\frac{3}{4}\right)-\left(\frac{9}{8}-\frac{9}{8}\right)\right\}+\frac{1}{2}\times \frac{1}{4}\times \frac{3}{4}$

$=\frac{1}{4}+\frac{3}{32}=\frac{11}{32}$