While buttering my bread at lunch one day I mused that one can not only cut a square pat of butter in half with only a knife, but also if the pat is in the shape of a regular n-gon, n>3. But what if the pat is shaped like an irregular quadrilateral?

Can you bisect the area of an arbitrary quadrilateral with one straight line using only a straightedge and a compass?

(In reply to Solution by Bractals)

Since you didn't explain your equation, I tried to figure it out for myself.  I got

|BG|^2=(1/4)|AC|(|BB'|+|DD'|)|BB'|^2.

One of us, at least, is wrong.  An example can identify whose wrong, but only a proof will confirm who is right.  Can you supply a proof?

Also, I think your analysis is incomplete unless you also show how to construct the square root of a number with only a straight edge and a compass.  Your equation requires obtaining a square root of a number to find G.

Posted by McWorter on 2005-08-16 22:02:03