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Let ABCD be a rectangle with sides AB = 3 and BC = 5.  The rectangle is folded so that C ends up on AB with AC = 2 and BC = 1.  Find the area of quadrilateral PCMN.

 

 

 Jan 5, 2021
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Let ABCD be a rectangle with sides AB = 3 and BC = 5.  The rectangle is folded so that C ends up on AB with AC = 2 and BC = 1.  Find the area of quadrilateral PCMN.

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Information of folded rectangle: 

 

AB =3      AC = 2        BC = 1         CM + BM = 5

 

CM2 - (5 - CM)2 = 1           CM = 2.6        BM = 2.4

 

∠ACP ≅ ∠BMC   ==>         β = tan-1(1/2.4)

 

DN = 2           AN = 3

 

[PCMN] = 6 1/15

 

            

 Jan 6, 2021

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