Question

ABCD is a rectangle. E, F, G and H are mid - point of sides AB, BC, CD and DA respectively. If ar (EFGH)= 16 cm2, find ar (ABCD).

Answer 1

Given that:- ABCD is a rectangle, E,F<G<H are the midpoints of AB,BC,CD,DA
Area of EFGH=16cm2

R.T.P   Ar of ABCD

construction:-join FH
 
Proof:-
in quad ABFH
Ar of EFH=1/2 Ar of ABFH.............1
in quad DCFH
Ar of GFH=1/2Ar ofDCFH..............2
from 1 and 2 we get
Ar of EFGH=1/2Ar of ABCD...........3
from 3 
Ar of ABCD =2 x 16 = 32cm2

Answer 2

hope it would be helpful