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In the figure, ABCD is a rectangle, AZ = WC = 6, AB = 15, and the area of trapezoid ZWCD is 130 square units. What is the area of triangle BQW?

 

 
 Jun 7, 2021
 #1
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Area of  ZWDC   =

 

130  =  (1/2)  ( DC) (WC + ZD)                    (DC = AB)

 

260  =  (15)  (  6  +  ZD)

 

260  / 15   = 6 +  ZD

 

52/3  =  6 +  ZD 

 

52/3 - 18/3  =  ZD

 

34/3  =  ZD  =   BW

 

And  triangle  BQW  is  congruent  to triangle   DQZ

 

So....the  height  of   BQW  =  AB/ 2  =    15/2

 

So  [BQW ]     =  (1/2) ( BW)  ( height)  =  (1/2) (34/3) ( 15/2)    =     85/2  =   42.5

 

cool cool cool

 
 Jun 7, 2021

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