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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.

 

 May 24, 2024
 #1
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Area of quadrilateral = AD *DC =  180

 

Shaded area  (a trapezoid) =  (1/2) AD * ( DC + DC/3)  =  (1/2) AD *(4/3)DC = (2/3) AD * DC

 

So....the shaded area  =  (2/3) (180)  =  120 

 

 

cool cool cool

 May 24, 2024

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