Question

abcd is a rectangle efgh are mid points of sides ab bc cd and da if area of efgh is 16 cm sq find area of abcd

Answer 1

Given that :- ABCD is a rectangle, E,F,G,H are m.p of AB, BC, CD, DA, Ar (EFGH) = 16.
To Find :- Ar (ABCD).
Construction:- Join FH.
Proof:-
Now,
In quad ABFH,
Ar (EFH) = 1/2 Ar (ABFH). ..................1).
Similarly in quad, DCFH,
Ar ( GFH ) = 1 /2 Ar (DCFH). ..............2).
From 1) and 2), we get:-
Ar (EFGH) = 1/2 Ar(ABCD). ...............3).

Therefore Ar ( EFGH ) = 16 cm^2 (given).
From 3, Ar (ABCD) = 2 x 16 = 32 cm^2


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