Answers

2016-02-24T19:04:11+05:30
M and N are midpoints of sides EF and DE.
∴ 2MN = DF and MN║DF (Midpoint theorem) ... (1)

In ΔDEF and ΔMEN,
=> ∠DEF = ∠MEN (common angle)
=> ∠EFD = ∠ENM (corresponding angles)
∴ ΔDEF is similar ΔMEN (By AA test for similarity)

Ratio of sides = MN/DF = MN/2MN = 1/2 (From 1)
∴ Ratio of areas = (Ratio of sides)² = (1/2)² = 1/4

∴ 1/4 = Ar(ΔMEN)/Ar(ΔDEF)
=> 1/4 = 4/Ar(ΔDEF)
=> 
Ar(ΔDEF) = 4*4 = 16 sq.cm
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