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

 Apr 22, 2022
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See the image below   (not to  scale)

 

 

The area of (1/2)  of the octagon =   (1/2) [ 2 * 12^2 ( 1 + sqrt 2)]  = 144 (1 + sqrt 2)

 

Triangle CDE  has an  area of   (1/2) CD * DE * sin 135°  =  (1/2) 12^2 sin 135° =   72 / sqrt 2 =  36sqrt (2)

 

So  the area of the trapezoid BCEF   =   

 

area of (1/2) octagon  -  area of triangle CDE

 

 144 ( 1 + sqrt 2)  - 36 sqrt 2  = 

 

[144 + 108sqrt 2] cm^2   ≈ 296.74 cm^2 

 

 

cool cool cool

 Apr 22, 2022

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