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 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
