Solution to Problem 247

Correct solutions came from BU students Colin Schulties, Kirstin Jerzy, Rob Andry and alumnus Will Shelton.  Correct solutions were sent in by Juan Carlos Marivela, Spain; Philippe Fondanaiche, France; Bill Webb, USA; Farid Lian, Colombia; Ron Welch, USA; Jerome Cherry; Yunting GAO, China; Jack Tseng; Ahron Teitelman, Israel; Lou Cairoli, USA; Claudio Baiocchi, Italy.

Almost all solvers of this problem assumed that the quadrilateral is a parallelogram, and therefore a rectangle. I will give a solution based on this assumption.  See Problem 251.

Using the fact that this is a quadrilateral and that ab = 1/4, we only need to determine bt.  Using Pythagoras, we have (ab)2 +(bt)2 = (ab)2 and so (1/4)2 + (bt)2 = (y + 1/4)2.  Looking at the radius through b and t we also have bt + y = 1/2.  Solving these two simultaneously gives y = 1/6 and bt = 1/3.  The area of the quadrilateral is 1/12.

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