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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?

 Dec 13, 2018
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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

 

 

cool cool cool

 Dec 13, 2018

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