Let ABC be any triangle. Let D be a point on side AB and let E be a point on side AC. Draw lines CD and BE and call their intersection F. Triangle ABC is then divided into three smaller triangles BDF, CEF, BCF and a quadrilateral ADFE.

Let the area of BDF equal r, the area of CEF equal q, and the area of BCF equal p. Express the area of the whole triangle ABC in terms of p, q, and r.

(In reply to easier "cheat" answer by Daniel)

Even when the points D and E are midpoints of their respective sides, the formula would be 2r+2q+p, as works out in Geometer's Sketchpad. Area p is the unusual one as not having a point D or E.

Posted by Charlie on 2008-11-30 15:42:29