Conversion of a convex polygon to a triangle using a compass and strait edge Given a convex polygon with 4 or more sides, is there a way to transform (convert, reduce) that polygon to a triangle having the same area as the polygon by using only a compass and straight edge?

For a tetragon $ABCD$, draw one of its diagonal, say $BD$, and put the orthogonal lines to this from the other two vertices, then add these heights $m_A$ and $m_C$ on one of these sides, along the orthogonal line, say the line of $m_A$, yielding a point $A'$. Then triangle $BCA'$ has the same area as the tetragon.
