21st Brazil 1999 Problem A1 ABCDE is a regular pentagon. The star ACEBD has area 1. AC and BE meet at P, BD and CE meet at Q. Find the area of APQD.
Let AD and CE meet at R, and AD and BE meet at S. Then PQDR is a parallelogram, so PQD and QRD are both half of the parallelogram and hence have equal areas. Hence area PQD = area ERS. So area APQD = area APQD - area PQD + area ERS = area APDRES = (area star)/2 = 1/2. 21st Brazil 1999 © John Scholes jscholes@kalva.demon.co.uk 4 April 2004 Last corrected/updated 4 Apr 04