jmc

Since $E$ is the midpoint of $BC$, $BE=EC$. Since triangles $△ABE$ and $△AEC$ have equal base length and share the same height, they have the same area.

$△ABC$ has $\frac{1}{2}$ the area of the rectangle, so the white triangle, $△AEC$, has $1/4$ the area of the rectangle.

Hence the shaded region has $1-\frac{1}{4}=\frac{3}{4}$ of the area of the rectangle, or $\boxed{75}\%$.