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Question Number 146494 by syamilkamil1 last updated on 13/Jul/21

Solid cube ABCD.EFGH is cut by a plane X so that it forms a plane of slices IJKLMN where I is mid AB, J is mid BF K is mid FG, L is mid HG, M mid DH and N mid AD. If the edge of the cube is X, find the area of the IJKLMN field

$$ \\ $$$$\mathrm{Solid}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{pla}{ne}\:{X}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{forms}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{slices}\: \\ $$$$\mathrm{IJK}{LM}\mathrm{N}\:\mathrm{where}\:\mathrm{I}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{AB},\:\mathrm{J}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{BF} \\ $$$$\:{K}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{FG},\:\:\mathrm{L}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{HG},\:\:\mathrm{M}\:\mathrm{mid}\:\mathrm{DH}\: \\ $$$$\mathrm{and}\:\mathrm{N}\:\mathrm{mid}\:\mathrm{AD}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{edge}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\: \\ $$$$\mathrm{is}\:{X},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{IJKLMN}\:\mathrm{field} \\ $$

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