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.

Guest Jan 12, 2020

#1**+1 **

Triangle(BPS) is similar to Triangle(BAC) ---> Area(BPS) / Area(BAC) = BP^{2} / BA^{2} = 2^{2} / 3^{2} = 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

geno3141 Jan 12, 2020