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\(ABCDEFGH\)  is a regular octagon of side 12cm. Find the area in square centimeters of trapezoid \(BCDE\). Express your answer in simplest radical form.


 

tertre  Mar 24, 2018
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 #1
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This is an isosceles trapezoid...angle  DEB   = 45° 

 

We can find the height, H,  of the tapezoid as

 

sin(45)  =  H / 12

12 sin (45)  = H

6√2   cm = H

 

And the longer base length is [12 + 6√2  + 6√2]  =   [ 12  + 12√2  ] cm

 

So....the area  is

 

height  *  (sum of base lengths)  / 2 =

 

6√2  [  12 + (12 +12√2) ] / 2  =

 

6√2 [ 24  + 12√2 ] / 2  =

 

3√2  [ 24  + 12√2]  =

 

72√2  + 72  =

 

72 (√2 + 1)  cm^2  

 

 

cool cool cool

CPhill  Mar 24, 2018
 #2
avatar+2347 
0

Thanks so much, CPhill! cool

tertre  Mar 24, 2018

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