What is the area of the shaded region in this rectangle?

The heights of $c$ and $d$ are in the ratio $1:3$ (equal to the ratio of their bases). So the heights are $1$ and $3$ respectively.

The area is $$3\times 4-\frac{1}{2}\times 1\times 4-\frac{1}{2}\times 1\times 4-\frac{1}{2}\times 1\times 1-\frac{1}{2}\times 3\times 3$$

For each of the shaded triangles, the length of a vertical line from the top corner until it hits the bottom side is $2$. The horizontal distance between the two other corners is $\frac 32$. So the area of each shaded triangle is $\frac12\cdot 2\cdot \frac32$.