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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.

 

 Mar 23, 2024
 #1
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Total area =  DC * AD

 

Area of triangles  ADU + BCT  = 2* (1/2)( DC/3) (AD)  =  DC * AD  /  3

 

Shaded area  =  DC*AD - DC * AD / 3  =  (2/3)DC *AD  = (2/3)(180) =  120

 

cool cool cool

 Mar 23, 2024

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