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?

Guest Dec 13, 2018

#1**+1 **

We can find DZ by using the formula for the area of a trapezoid

120 = (1/2) (DC) (WC + DZ) and (DC = AB) so we have

120 = (1/2) (12) (6 + DZ)

120 = 6 (6 + DZ)

20 = 6 + DZ

14 = DZ = BW

Note that, by ASA, triangle BQW is cogruent to triangle DQZ

So....their altitudes are equal = (1/2)AB = 6

So.....the area of triangle BQW = (1/2)BW (6) = (1/2)(14)(6) = (1/2)84 = 42 units^2

CPhill Dec 13, 2018