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On the inside of a square with side length 6, construct four congruent isosceles triangles each with base 6 and height 5, and each having one side coinciding with a different side of the square. The area of the octagonal region common to the interiors of all four triangles is
Correct Answer: 3.6
By symmetry, consider one corner of the common octagonal region and let the relevant small lengths be $$x$$ and $$y$$. The triangle geometry gives $$5x=3y$$, while the side condition gives $$\frac{6}{5}-x=y$$. Solving gives $$x=\frac{9}{20}$$ and the resulting octagonal area is $$3.6$$ square units.
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