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# ABCD is a rectangle

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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\$? Jan 4, 2021

#4
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Jan 4, 2021

### 4+0 Answers

#1
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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

Jan 4, 2021
#2
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Very nice, JoLink....!!!!   CPhill  Jan 4, 2021
#3
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It is good that you like it Chris, it is your answer.

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

JoLink, do not take the credit for other people's answers!

Just say that you have found an answer by CPhill and give the link.

You will be given credit for your research skills and your willingness to help.

Linking a question to a good question will give you a good name.

Taking credit for other people's answers is plagiarism. It is immoral and very rude.

Taking credit for other people's work gives you a bad name.

Jan 4, 2021
edited by Melody  Jan 4, 2021
#4
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Best Answer

See CPhill's answer

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

Melody Jan 4, 2021