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Folding problem of mathematical geometry in junior high school
Above, FH⊥AD,H is vertical foot; EF is the middle vertical line of AM, an = nm = am/2;

AM/AE=AD/AN from Rt⊿ADM∽Rt⊿ANE, or AE=AM*AN/AD=AM? / 16=(8? +x？ )/ 16,

He = DM = x from RT ⊿ FHE ≌ RT ⊿ ADM;

BF = AH = AE-HE； BF+AE=2AE-HE=(8？ +x？ )/8-x

The area of trapezoidal ABFE is S=AB*(BF+AE)/2=4(BF+AE)=(8? +x？ )/2-4x=x？ /2-4x+32。 ,

The area of trapezoidal CDEF y=AB? -S=64-(x？ /2-4x+32)=-x？ /2+4x+32 .

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