In the figure, $ABCD$ is a rectangle, $AZ = WC = 6, AB = 12,$ and the area of trapezoid

$ZWCD$ is $120$ square units. What is the area of triangle $BQW$?

Guest Jan 4, 2021

#1**+1 **

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 subtract 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

JoLink Jan 4, 2021

#3**+1 **

It is good that you like it Chris, it is your answer.

https://web2.0calc.com/questions/help_7273

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Melody Jan 4, 2021