1. ABCD is a  trapezium with parallel sides AB=a and DC=b. If E and F are midpoints of non-parallel sides AD and BC respectively, then the ratio of areas of quadrilaterals ABFE and EFCD is??

Asked by kumar.ashlesha | 12th Dec, 2014, 08:45: PM

Expert Answer:

Consider the following figure.
G i v e n space t h a t space A B N equals a comma space C D equals b L e t space h space b e space t h e space h e i g h t space o f space t h e space t r a p e z i u m space A B C D T h u s space h e i g h t space o f space t h e space t r a p e z i u m space E F B A equals h over 2 A r e a space o f space t h e space t r a p e z i u m space A E F B equals 1 half open parentheses a plus b plus E X plus Y F close parentheses cross times h over 2 S i m i l a r l y comma space space h e i g h t space o f space t h e space t r a p e z i u m space E D C F equals h over 2 A r e a space o f space t h e space t r a p e z i u m space E D C F equals 1 half open parentheses b plus b plus E X plus Y F close parentheses cross times h over 2 T h u s comma space r a t i o space o f space Q u a d left parenthesis A B F E right parenthesis space a n d space q u a d left parenthesis E F C D right parenthesis space equals fraction numerator 1 half open parentheses a plus b plus E X plus Y F close parentheses cross times h over 2 over denominator 1 half open parentheses b plus b plus E X plus Y F close parentheses cross times h over 2 end fraction rightwards double arrow r a t i o equals fraction numerator open parentheses a plus b plus fraction numerator a minus b over denominator 2 end fraction close parentheses over denominator open parentheses b plus b plus fraction numerator a minus b over denominator 2 end fraction close parentheses end fraction space space space space rightwards double arrow r a t i o equals fraction numerator 2 a plus 2 b plus a minus b over denominator 2 b plus a minus b end fraction space space rightwards double arrow r a t i o equals fraction numerator 3 a plus b over denominator a plus 3 b end fraction space space space

Answered by Vimala Ramamurthy | 13th Dec, 2014, 12:29: PM