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In the diagram below, each side of convex quadrilateral $ABCD$ is trisected.  (For example, $AP = PQ = QB.$)  The area of convex quadrilateral $ABCD$ is $180.$  Find the area of the shaded region.

 

 Dec 29, 2023
 #1
avatar+129270 
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AD * AB  =180

 

The shaded area is a  trapezoid with bases of  AB,  AB/3    and  height AD

 

Its area =

 

(1/2)(AD)(AB + AB/3)  =

 

(1/2)(AD)(4/3)(AB)  =

 

(2/3) AD * AB  =     (2/3)(180) =  120

 

 

cool cool cool

 Dec 29, 2023

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