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In the diagram, AB, BC, CD, DE, EF, FG, GH, and HK all have length 4, and all angles are right angles, with the exception of the angles at D and F.  Find the area of the polygon.

 

 

\(\phantom{what is x^2}\)

 Jul 1, 2022
 #1
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Draw DF  and CG

 

Really....the only  trick here is to find  DF = sqrt [ 4^2 + 4^2 ] = sqrt (32) = 4sqrt 2 = CG

 

Area of BHKA  =  [ BA *  (BC + DF + GH) ]   =  [ 4 * ( 4 + 4sqrt 2 + 4) ]  =  [ 4 ( 8 + 4sqrt 2 )  = 

32 + 16sqrt 2  

 

Area of rectangle DFGC  =  FG * DF =   4 * 4sqrt 2 =  16sqrt 2

 

Area of right triangle DFE  = (1/2) * DE * FE =  (1/2) * 4^2 =  8

 

Area of  DEFGC =  16sqrt 2  - 8  

 

Area of   polygon  =

 

32 +16sqrt 2 + 16sqrt 2  - 8  =

 

24 + 32sqrt 2

 

 

cool cool cool

 Jul 1, 2022

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