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Let ABCD be a convex quadrilateral, and let P, Q, R, S, T, U, V, and W be points that trisect the sides of ABCD, as shown.

 


If the area of quadrilateral  ABCD is 180  then find the area of hexagon APSCTW.

 

 Jan 12, 2020
 #1
avatar+18964 
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Triangle(BPS) is similar to Triangle(BAC)     --->     Area(BPS) / Area(BAC)  =  BP2 / BA2  =  22 / 32  =  4/9

     Consequently, Area(APSC)  =  5/9 · Area(ABC)

 

Similarly, Area(DWT) / Area(DAC)  =  4/9     --->     Area(WACT)  =  5/9 · Area(DAC)

 

Therefore, Area(APSCTW)  =  5/9 · Area(ABCD)     --->     Area(APSCTW)  =  5/9 · 180  =  20

 Jan 12, 2020
 #2
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It says incorrect

Guest Jan 12, 2020
 #3
avatar+108771 
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Nothing like good manners and graciousness. ... That is sarcasm.

Note: I would not bother responding more to you.

 

I don't know if it is right or wrong but thanks for your efforts Geno.

Melody  Jan 12, 2020
 #4
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oh, I got it now, it was 100, not 20, thank you

Guest Jan 13, 2020

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