Area del trapecio AM-GM

No me interesa de aquí el area en sí sino la demostración tan elegante

http://i113.photobucket.com/albums/n205/leonsotelo/Areatrapecio.jpg

http://jwilson.coe.uga.edu/emt725/Isos.Trpzd/Diag/diag.html

http://jwilson.coe.uga.edu/emt725/Class/Lanier/ISOSTRAP/isotrap.html

http://www.artofproblemsolving.com/Forum/viewtopic.php?t=145287

http://www.artofproblemsolving.com/Wiki/index.php/Root-square-mean_arithmetic-mean_geometric-mean_harmonic-mean_inequality