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ICSE Class 9 Answered

abcd is a parallelogram . bp:pc=1:2 area of cpq=20 cm² find the area of cdp and abcd
Asked by rgkgmu | 06 Feb, 2016, 02:33: PM
answered-by-expert Expert Answer
begin mathsize 14px style C o n s t r u c t i o n colon space D r a w space C L perpendicular D Q A left parenthesis triangle C P Q right parenthesis equals 1 half cross times b a s e cross times a l t i t u d e equals 1 half cross times P Q cross times C L A left parenthesis triangle D C P right parenthesis equals 1 half cross times D P cross times C L N o w comma space fraction numerator A left parenthesis triangle C P Q right parenthesis over denominator A left parenthesis triangle D C P right parenthesis end fraction equals fraction numerator P Q over denominator D P end fraction space space space space space space... left parenthesis 1 right parenthesis S i n c e space D C space i s space p a r a l l e l space t o space A Q space a n d space B C space i s space t h e space t r a n s v e r s a l comma angle D C P equals angle Q B P space space space space space..... left parenthesis a l t e r n a t e space i n t e r i o r space a n g l e s right parenthesis I n space triangle D C P space a n d space triangle Q B P comma angle D C P equals angle Q B P angle D P C equals angle Q P B space space space space.... left parenthesis V O A right parenthesis rightwards double arrow triangle D C P tilde triangle Q B P space space space space space space.... left parenthesis A A space T e s t right parenthesis rightwards double arrow fraction numerator P C over denominator B P end fraction equals fraction numerator D P over denominator P Q end fraction equals fraction numerator C D over denominator B Q end fraction space space space space... left parenthesis c s c t right parenthesis rightwards double arrow fraction numerator P C over denominator B P end fraction equals fraction numerator D P over denominator P Q end fraction rightwards double arrow 2 over 1 equals fraction numerator D P over denominator P Q end fraction rightwards double arrow fraction numerator P Q over denominator D P end fraction equals 1 half F r o m space left parenthesis 1 right parenthesis comma space fraction numerator A left parenthesis triangle C P Q right parenthesis over denominator A left parenthesis triangle D C P right parenthesis end fraction equals 1 half rightwards double arrow fraction numerator 20 over denominator A left parenthesis triangle D C P right parenthesis end fraction equals 1 half rightwards double arrow A left parenthesis triangle D C P right parenthesis equals 40 space c m squared end style
 
begin mathsize 14px style N o w comma space p a r a l l e log r a m space A B C D space a n d space triangle D C Q space h a v e space s a m e space b a s e space D C space a n d space b e t w e e n space s a m e space p a r a l l e l s D C space a n d space A Q comma T h u s comma space w e space h a v e A r e a space o f space p a r a l l e log r a m space A B C D equals 2 cross times A left parenthesis triangle D C Q right parenthesis equals 2 cross times left square bracket A left parenthesis triangle D C P right parenthesis plus A left parenthesis triangle C P Q right parenthesis right square bracket equals 2 cross times left square bracket 40 plus 20 right square bracket equals 2 cross times 60 equals 120 space c m squared end style
Answered by Rashmi Khot | 08 Feb, 2016, 12:48: PM

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