I am looking for an easy derivation for the area of an obtuse triangle. As everybody knows the formula for any triangle is the same: half the product of the base and its height. The derivation for an acute triangle is quite neat and purely geometrical (you draw a rectangle twice the size of the triangle and are done). I am looking for an equally simple derivation for the area of an obtuse triangle. Just to be clear I don't have a problem deriving this in all kinds of ways (including using integrals). However the simplest I found would still require either to solve a set of linear equations or the distributive law. Is it possible to do it without these?
