question_answer

If E, F, G and H are respectively the mid points of the sides of a parallelogram ABCD and ar\[(EFGH)=40c{{m}^{2}},\]find the ar (parallelogram ABCD).

A) \[~40\,c{{m}^{2}}\]                       

B) \[~20\,c{{m}^{2}}\]           

C)   \[~80\text{ }c{{m}^{2}}\]             

D)   \[~60\text{ }c{{m}^{2}}\]

Correct Answer: C

Solution :

Joint HF, Then \[HF||AB||CD\] \[\Rightarrow \]\[ar(\Delta FGH)=\frac{1}{2}(HFCD)\]        ?.(i) \[\Rightarrow \]\[ar(\Delta \Epsilon FH)=\frac{1}{2}(ABFH)\]          ?.(ii) From (i) and (ii),we get \[ar(EFGH)=\frac{1}{2}(ABCD)\] \[\Rightarrow \]\[40=\frac{1}{2}(ABCD)\] \[\Rightarrow \]\[80\,c{{m}^{2}}=ABCD\]