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In the figure, ABCD is a rectangle, AZ=WC=6 units, AB=12 units and the area of trapezoid ZWCD is 120 square units. What is the area of triangle BQW?

 

 Nov 21, 2018
 #1
avatar+107348 
+1

Since the area of the trapezoid   ZWCD is 120

The height of this trapezoid is AB and the bases are ZD and WC

We have

 

120 = (1/2) AB  (ZD + WC)

120 = (1/2) 12 ( ZD + 6)     multiply through by 2

240 = 12 (ZD + 6)      divide both sides by 12

20 =  ZD + 6       ubtract 6 from both sides

14 = ZD

 

Now   angle DBW = angle BDZ

And angle ZQD = angle BQW

And since AZ = WC

Then  ZD = BW

 

So by AAS....triangle ZQD is congruent to triangle WQZ

 

And the altitude of trangle DQZ    = altitude of triangle BQW

And since twice these altitudes = AB....then each altitude = 1/2(AB) = 6

 

So....the area of triangle BQW   =

 

(1/2) BW * altitude of BQW   = 

 

(1/2) (14)(6) =

 

(1/2) (84) =

 

42 units^2

 

 

cool cool cool

 Nov 21, 2018
edited by CPhill  Nov 21, 2018
 #2
avatar+128 
+1

guarteed 42

 Nov 21, 2018

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