class 9 chapter parallelogram exercise 2 level one ka ques no. 2
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Q.2 If E, F, G and H are respectively the mid- points of the sides of a parallelogram ABCD, show that ar(EFGH) =12ar(ABCD)
Sol. Δ HGF and || gm HDCF stand on the same base HF and lie between the same parallels HF and DC.
8Therefore, ar(ΔHGF) = 12ar(HDCF) ... (1)
Similarly, Δ HEF and ||gm ABFH stand on the same base HF and lie between the same parallels
HF and AB.
Therefore ar(ΔHEF) = 12ar(ABFH) ... (2)
Therefore Adding (1) and (2), we get
ar(ΔHGF) + ar(ΔHEF) = 12ar(HDCF) + ar(ABFH)
⇒ ar(EFGH) = 12ar(ABCD)
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