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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.

 

 Jan 7, 2024
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[ABCD] = AD * DC  =   180

 

The shaded area is a trapezoid with area  =   (1/2) AD (AB + UT)  and AB = DC and UT = DC / 3  

 

So....the shaded area =  (1/2)(AD) (DC + DC/3)  =  (1/2)(AD)(DC)   + (1/2)(AD)(DC//3)  =

 

90  +  (1/6)(AD)(DC)  = 

 

90  +  30   =

 

120

 

cool cool cool

 Jan 7, 2024

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