Question

In ∆GHK; D, E and F are the mid-point of sides HK, KG and GH respectively, show that EFHK is trapezium and ar (EFHK) = 3/4ar (∆GHK)
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Answer 1

E and F are midpoints

by midpoint theorem,

FE || KH

FE=1/2 KH

as 2sides of a quadrilateral are parallel, EFHK is a trapezium

ar(EFHK)= ar(DEF)+ar(DEK)+ar(DFH)= 3[1/4 ar(∆GHK)]

= 3/4 ar (∆GHK)

BECAUSE ar of ∆DEF = ar of ∆DFH = ar of ∆DEK = 1/4 [ar of ∆GHK]