1998 AHSME Problem 8
A square with sides of length 1 is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the center of the square with points on three of the sides, as shown. Find x, the length of the longer parallel side of each trapezoid.
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1 solution
The symmetry suggests that the point inside is actually the square centre. Then we can say: (1-x) 1+ (x-1/2)/2 = 1/3 or (x+1/2) 1/2*1/2 =1/3. Either way, x = 5/6