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D, E and F are respectively the mid-points of the sides BC, CA and AB of a ∆ ABC. Show that (iii) ar (BDEF) = 1/2 ar (ABC)

Q: 5    D, E and F are respectively the mid-points of the sides BC, CA and AB of a \small \Delta ABC. Show that

          (iii) \small ar(BDEF)=\frac{1}{2}ar(ABC)

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M manish


Since we already proved that,
ar(\DeltaDEF) = ar (\Delta BDF).........(i)

So, ar(||gm BDEF) = ar(\DeltaBDF) + ar (\DeltaDEF)
                               = 2 . ar(\DeltaDEF)    [from equation (i)]
                               \\= 2[\frac{1}{4}ar(\Delta ABC)]\\ =\frac{1}{2} ar(\Delta ABC)

Hence proved.

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