jmc

Since we are dealing with fractions of the whole area, we may make the side of the square any convenient value. Let us assume that the side length of the square is $4.$ Therefore, the area of the whole square is $4\times 4=16.$

The two diagonals of the square divide it into four pieces of equal area so that each piece has area $16÷4=4.$

The shaded area is made up from the "right" quarter of the square with a small triangle removed, and so has area equal to $4$ minus the area of this small triangle. This small triangle is half of a larger triangle. This larger triangle has its base and height each equal to half of the side length of the square (so equal to $2$) and has a right angle. So the area of this larger triangle is $\frac{1}{2}\times 2\times 2=2.$

So the area of the small triangle is $\frac{1}{2}\times 2=1,$ and so the area of the shaded region is $4-1=3.$

Therefore, the shaded area is $\boxed{\frac{3}{16}}$ of the area of the whole square.