Help with Geometry

First, cut up the triangle into smaller triangles of the same size like so:

Then, find the fraction of the shaded triangles/all triangles: 

You will get an answer of 6/16, which simplifies to 3/8

Hope this helps! If I made a mistake please correct me :)

That looks pretty cool Milkcloud,  lets see if it I can validate it.

I let the perpendicular distance between each trapezium be 1 unit

The total area is   0.5*4a*4 = 8a units squared

The top triangle is     0.5*a*1 = 0.5a   units squared

The middle trapezium area is    (2a+3a)/2  *1 = 5a/2

The sum of the top triangle and the middle trapezium is     a/2  +    5a/2    = 3a

The fraction of the whole figure this is is        3a /  8a = 3/8

So it seems your method works very nicely Milkcloud.