+1242 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?
+128474 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
