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CBSE Class 9 Answered

ABCD is a trapiziuem in which parrallel sides AB is 25cm. DC equal to 10cm. and non parrallel side AD equal to 14 cm. and BC equal to 13cm. Find the area of trapiziuem ABCD.
Asked by ashokkumar698 | 05 Aug, 2014, 09:13: PM
answered-by-expert Expert Answer
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.
D r a w space a space l i n e space C E space p a r a l l e l space t o space A D. T h u s comma space A D equals C E equals 14 space c m. T h e r e f o r e comma space t h e space a r e a space o f space t h e space t r a p e z i u m space A B C D equals A r e a space o f space t h e space p a r a l l e log r a m square space A E C D plus A r e a space o f space t h e space t r i a n g l e triangle space B C E T h e space t r i a n g l e space B C E space i s space h a v i n g space s i d e s space 13 space c m comma space 14 space c m space a n d space 15 space c m. L e t space u s space f i n d space t h e space a r e a space o f space t h e space t r i a n l g e space B C e space u sin g space h e r o n apostrophe s space f o r m u l a. s equals fraction numerator a plus b plus c over denominator 2 end fraction H e r e comma space a equals 13 space c m comma space b equals 14 space c m comma space a n d space c equals 15 space c m T h u s comma space s equals fraction numerator 13 plus 14 plus 15 over denominator 2 end fraction equals 21 space c m A r e a space o f space t h e space t r i a n g l e space B C E equals square root of s open parentheses s minus a close parentheses open parentheses s minus b close parentheses open parentheses s minus c close parentheses end root rightwards double arrow A r e a space o f space t h e space t r i a n g l e space B C E equals square root of 21 open parentheses 21 minus 13 close parentheses open parentheses 21 minus 14 close parentheses open parentheses 21 minus 15 close parentheses end root rightwards double arrow A r e a space o f space t h e space t r i a n g l e space B C E equals square root of 21 cross times 8 cross times 7 cross times 6 end root rightwards double arrow A r e a space o f space t h e space t r i a n g l e space B C E equals square root of 7056 rightwards double arrow A r e a space o f space t h e space t r i a n g l e space B C E equals 84 space c m squared A r e a space o f space t h e space t r i a n g l e space B C E equals 1 half cross times b a s e cross times h e i g h t rightwards double arrow 84 equals 1 half cross times B E cross times C F rightwards double arrow 84 cross times 2 equals 15 cross times C F rightwards double arrow C F equals fraction numerator 84 cross times 2 over denominator 15 end fraction W e space k n o w space t h a t space a r e a space o f space t h e space t r a p e z i u m space A B C D equals 1 half cross times h e i g h t cross times open parentheses a plus b close parentheses rightwards double arrow space a r e a space o f space t h e space t r a p e z i u m space A B C D equals 1 half cross times C F cross times open parentheses 10 plus 25 close parentheses rightwards double arrow space a r e a space o f space t h e space t r a p e z i u m space A B C D equals 1 half cross times fraction numerator 84 cross times 2 over denominator 15 end fraction cross times 35 equals 196 space c m squared
Answered by Vimala Ramamurthy | 07 Aug, 2014, 10:48: AM

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