Answer :


AC = CE = EF = AF = 4 cm


B is midpoint of AC


AB = BC = 1/2 AC


AB = BC = 1/2 × 4 cm


AB = BC = 2 cm


Similarly,


D is midpoint of AC


CD = DE = 1/2 CE


CD = DE = 1/2 × 4 cm


CD = DE = 2 cm


AE is diagonal of ACEF,


By Pythagoras theorem,


AF2 + EF2 = AE2


42 + 42 = AE2


AE2 = 16 + 16


AE2 = 32


AE= √32


AE= 4√2 cm


J is midpoint of AE,


AJ = JE = 1/2 AE


AJ = JE = 1/2 × 4√2 cm


AJ = JE = 2√2 cm


G is midpoint of AJ,


AG = JG = 1/2 AJ


AG = JG = 1/2 × 2√2 cm


AG = JG = √2 cm


BGJH is a square


BG = JH = HB = JG = √2 cm


Also,


HD = HB = √2 cm


And,


IE = IJ = GJ =√2 cm


HD and IE are equal and parallel


HDEI is a parallelogram


HI = DE = 2 cm


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