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?

Lightning
Nov 21, 2018

#1**+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

CPhill
Nov 21, 2018