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ABCDEFGH is a regular octagon of side 12cm. Find the area in square centimeters of trapezoid BCEF.

 Nov 16, 2020
 #1
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https://web2.0calc.com/questions/abcdefgh-is-a-regular-octagon-of-side-12cm

 Nov 16, 2020
 #2
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Let's see how the guest derived his/her answer.....

 

Look at the following:

 

 

The area we seek  is (1/2)  the area of the octagon  less the area of  triangle CDE

 

Note that angle CDE = 135°

 

Area of triangle  CDE =  (1/2) (CD) (DE) sin (135)  = (1/2) (12) (12) ( 1/ sqrt(2))  = 72/sqrt (2)  = 36sqrt (2)   [1]

 

Area of (1/2) of the octagon =  ( 1 + sqrt (2) ) * side^2  =  (1 + sqrt (2) ) (12)^2  =  (1 + sqrt (2) ) (144)  =

 

144 + 144sqrt (2)     [2]

 

Area of trapezoid =     [2]  - [1]   =    [ 144 + 108 sqrt (2)] cm^2  ≈  296.735 cm^2

 

 

cool cool cool

 Nov 16, 2020

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