If you make the paper translucent, you will see that in the $M$ shape contains a flat isosceles triangle $T$. Dividing $T$ into half gives a right triangle that is similar to the half of the paper rectangle. The ratio between the sides is $\frac{3\sqrt{13}}{18}$, so the area of $T$ is $2\cdot\frac{13}{36}\cdot 108=78$ Consider half the region inside the M shaped region but outside $T$. This region has area $108-78=30$ So the area of $M$ region is $30*2+78=\boxed{138}