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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 28, 2024

Best Answer 

 #1
avatar+394 
+2

Note: I will use [] to denote area.

[ABCD] = AD * DC

[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6

[ADU]+[BCT]=AD*DC/3

[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = 120.

 Mar 29, 2024
 #1
avatar+394 
+2
Best Answer

Note: I will use [] to denote area.

[ABCD] = AD * DC

[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6

[ADU]+[BCT]=AD*DC/3

[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = 120.

hairyberry Mar 29, 2024

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