Minimum Area of a Folded Square

★ 5/10plane geometry Extrema Reflection Completing the Square

Problem

A square sheet of paper $ABCD$ with side length $1$ is folded so that vertex $B$ lands at a point $B'$ on side $AD$ , as shown in the figure. The crease meets sides $AB$ and $CD$ at points $E$ and $F$ respectively, so the part of the paper that is folded over is the quadrilateral $EBCF$ . Find the minimum possible area of the folded part.

Answer

Solution

Difficulty	5/10
Topics	plane geometry, Extrema, Reflection, Completing the Square

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