In the figure, ABCD is a rectangle, AZ = WC = 6, AB = 15, and the area of trapezoid ZWCD is 130 square units. What is the area of triangle BQW?
+129847 Area of ZWDC =
130 = (1/2) ( DC) (WC + ZD) (DC = AB)
260 = (15) ( 6 + ZD)
260 / 15 = 6 + ZD
52/3 = 6 + ZD
52/3 - 18/3 = ZD
34/3 = ZD = BW
And triangle BQW is congruent to triangle DQZ
So....the height of BQW = AB/ 2 = 15/2
So [BQW ] = (1/2) ( BW) ( height) = (1/2) (34/3) ( 15/2) = 85/2 = 42.5
