+0

# ABCD is a rectangle

0
110
4

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
+112827
0
Jan 4, 2021

#1
+86
+2

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
+117573
0

CPhill  Jan 4, 2021
#3
+112827
+1

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

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

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
+112827
0