In the figure, ABCD is a rectangle, AZ=WC=6 units, AB=12 units and the area of trapezoid ZWCD is 150 square units. What is the area of triangle BQW?
We can find DZ thusly
150 = (1/2) AB * ( WC + DZ)
150 = (1/2) 12 * ( 6 + DZ)
150 = 6 * ( 6 + DZ)
150/ 6 = 6 + DZ
25 - 6 = DZ = 19 = BW
And triangles DQZ and BQW are congruent,,,,so their heights are congruent = 12/ 2 = 6
So....the area of triangle BQW = (1/2) BW * 6 = (1/2) (19) (6) = 57