Trapezium Equation

[Xilef]

I'm trying to program chamfers into one of my game engines, I've got a neat method which involves drawing a trapezium, however I'm stuck with this equation!

I know the lengths of lines A, B and C, how do I find the length of D and E?
EDIT: I know how far along line C the lines D and E are

 

[Ellie]

If you know how far along they are just treat the section a to d as one trapezium, ignoring the rest. To get the height along c...

I assume, or this is how I would do it, treat it all proportionally. If d is 30x along the white line, then divide it by the length of the slanted line and multiply it by the length of the blue line c.

For the length of the slanted line treat the slanted line, c, and a as a triangle...

I'm confusing myself and that probably isn't helpful but idk, that's how I'd go about solving it.

 

[Prexus]

For anyone who lives in north america, this is called a Trapezoid.

 

[Xilef]

My best friend (A maths pro) helped me with it.

X = Distance line D is from B along C
X(A-B) + B = D
,,,,C

D = Line we're trying to find height with.

 

[Ellie]

Oh that's cool. (I should really know all this, just did it lol)