find the area of a regular hexagon ABCDEF in which each side measures 5 cm and whose height is 11 cm.

Asked by anujain0161 | 7th Sep, 2015, 04:19: PM

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.
A r e a space o f space H e x a g o n space A B C D E F equals A r e a space o f space triangle A B F plus A r e a space o f space square B C E F plus A r e a space o f space triangle C D E 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 space space space space space space space space equals 2 A r e a space o f space triangle A B F plus A r e a space o f space square B C E F S i n c e space A B C D E F space i s space a space r e g u l a r space h e x a g o n comma space triangle A B F space i s space a n space i s o s c e l e s space t r i a n g l e space w i t h space A F equals A B equals 5 space c m A l s o space g i v e n space t h a t space B F equals 11 space c m. I n space a n space i s o s c e l e s space t r i a n g l e comma space t h e space p e r p e n d i c u l a r space b i s e c t s space t h e space b a s e. T h u s comma space B M equals F M equals 11 over 2 equals 5.5 space c m I n space a space r i g h t space t r i a n g l e comma space h y p o t e n u s e space i s space t h e space l o n g e s t space s i d e. C o n s i d e r space t h e space t r i a n g l e comma space A F M colon A F equals 5 c m space a n d space F M equals 5.5 space c m S i n c e space 5.5 greater than 5 comma space w e space h a v e top enclose F M end enclose greater than top enclose A F end enclose comma space w h i c h space i s space i n c o r r e c t. space A F space s h o u l d space b e space l o n g e r space t h a n space o t h e r space t w o space s i d e s. T h e r e f o r e comma space t h e space d a t a space g i v e n space i n space t h e space p r o b l e m space i s space i n c o r r e c t. P l e a s e space c h e c k space t h e space q u e s t i o n.

Answered by Vimala Ramamurthy | 7th Sep, 2015, 05:20: PM

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