Not that much cluster, neat information.

To find the area of the shaded triangle in the diagram, we have to subtract the area of the unshaded triangles from the area of the whole square.

First, we need to find the area of all triangles, then add them up to receive the total area.

1st unshaded triangle(biggest triangle)= We use our trusty formula \(\frac{1}{2}*b*h\) . Plugging the values in, we have:

\(\frac{1}{2}*3x*4x=6x^2\).

2nd unshaded triangles(medium sized)=\(\frac{1}{2}*4x*2x=4x^2\) . The 2x came from 4x/2, because M is the midpoint of the side.

3rd unshaded triangle(smallest triangle)=\(\frac{1}{2}*x*2x=x^2\)

Now, we can add all the values up: \(6x^2+4x^2+x^2=11x^2\)

But, we're not done yet! We have to subtract the unshaded area(already found) from the total area of the square.

The area of the total square is:\(4x*4x=16x^2\) , since 4x is the side.

Thus, the area of the shaded triangle is:\(16x^2-11x^2=\boxed{5x^2}\)