Question
Fri March 20, 2015 By: Rrdave2611 Dave

two paralleograms are on equal bases and between same paralles. the ratio of their areas is 1:1. prove it
 

Expert Reply
Vimala Ramamurthy
Sun March 22, 2015
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
I n space t h e space a b o v e space f i g u r e comma space A B C D space a n d space A B F E space a r e space p a r a l l e log r a m s space w i t h space t h e space s a m e space b a s e space A B W e space k n o w space t h a t space t h e space a r e a space o f space t h e space p a r a l l e log r a m equals b a s e cross times d i s tan c e space b e t w e e n space t h e space p a r a l l e l space s i d e s.  N o w space a r e a left parenthesis square A B C D right parenthesis equals A B cross times h e i g h t  A n d space a r e a left parenthesis square A B F E right parenthesis equals A B cross times h e i g h t  T h e r e f o r e comma space a r e a left parenthesis square A B C D right parenthesis equals a r e a left parenthesis square A B F E right parenthesis rightwards double arrow fraction numerator a r e a left parenthesis square A B C D right parenthesis over denominator a r e a left parenthesis square A B F E right parenthesis end fraction equals 1 rightwards double arrow fraction numerator a r e a left parenthesis square A B C D right parenthesis over denominator a r e a left parenthesis square A B F E right parenthesis end fraction equals 1 over 1 rightwards double arrow a r e a left parenthesis square A B C D right parenthesis space colon space a r e a left parenthesis square A B F E right parenthesis equals 1 space colon space 1
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