Basically we need to establish two relationships before we can figure out what K is.

Height (h) = (Base + Hypotenuse)/2

k*(h^2) = (Base*Height)/2 = Area of a right triangle

Now we have to use the Pythagoras theorem to make the 1st relationship simpler. i.e. find substitute expressions for Hypotenuse.
We know that, Hypotenuse^2 = Height^2 + Base^2 . You can solve this to get the following expression: Hypotenuse = (h^2 + b^2)^1/2 . This can be substituted in the 1st relationship to get : b = 3h/4.
Finally we can use substitution one last time in the 2nd relationship in order to find k.
So we replace the Base value as follows, (3h/4*h)/2 = kh^2
H^2 gets cancelled from LHS and RHS. Giving you k value as 3/8.