Question

If E,F,G,and H are respectively the mid-points of the sides of a parallelogram ABCD, show that
ar(EFGH)=1/2 ar(ABCD)..

Answer 1

hope this answer helps you

Answer 2

contruct HF// AB//CD

NOW ,
ar. tri. NEM = 1/2 ar. //gm ABFH. ................. ( triangle inside a //gm ABFH & on same base MN)----------------(1)

Similarly,
ar. tri. HGF = 1/2 ar. tri. //gm HFDC. ----------------(2)

SO, BY ADDING (1) & (2),
ar EFGH = 1/2 ar .ABCD.

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