1st Centromerican 1999 Problem B1 ABCD is a trapezoid with AB parallel to CD. M is the midpoint of AD, ∠MCB = 150 o , BC = x and MC = y. Find area ABCD in terms of x and y.
xy/2 Solution Extend CM to meet the line AB at N. Then CDM and NAM are congruent and so area ABCD = area CNB. But CN = 2y, so area CNB = ½ 2y·x·sin 150 o = xy/2. 1st OMCC 1999 © John Scholes jscholes@kalva.demon.co.uk 26 November 2003 Last corrected/updated 26 Nov 03