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.