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Find ther area of the polygon

Asked by siddharth | 11th Jul, 2015, 06:04: PM

Expert Answer:

$C o n s i d e r space t h e space g i v e n space f i g u r e. W e space n e e d space t o space f i n d space t h e space a r e a space o f space t h e space p o l y g o n space A B C D E F A. T h e space g i v e n space p o l y g o n space i s space d i v i d e d space i n space t o space s m a l l e r space t r i a n g l e s. T h u s comma space A r e a open parentheses A B C D E F A close parentheses equals A r e a open parentheses A B F close parentheses plus A r e a open parentheses B C F close parentheses plus A r e a open parentheses C D F close parentheses plus A r e a open parentheses D E F close parentheses 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 t r i a n g l e space f o r m u l a space i s space 1 half cross times B a s e cross times A l t i t u d e therefore A r e a open parentheses A B C D E F A close parentheses equals 1 half cross times B F cross times A l t i t u d e space o f increment A B F plus 1 half cross times C F cross times A l t i t u d e space o f triangle B C F space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus 1 half cross times C F cross times A l t i t u d e space o f triangle C D F plus 1 half cross times D F cross times A l t i t u d e space o f triangle D E F space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator up diagonal strike 2 end fraction cross times 6.5 cross times up diagonal strike 2 plus 1 half cross times 7 cross times 4 plus 1 half cross times 7 cross times 4 plus fraction numerator 1 over denominator up diagonal strike 2 end fraction cross times 5 cross times up diagonal strike 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 6.5 plus 7 cross times 4 plus 5 space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 6.5 plus 28 plus 5 space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 39.5 space c m squared space space space T h u s comma space a r e a space o f space t h e space p o l y g o n space A B C D E F A space i s space 39.5 space c m squared. space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space$

Answered by Vimala Ramamurthy | 12th Jul, 2015, 09:56: AM

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