Let $abcd$ be a convex quadrilateral, and let $p$, $q$, $r$, $s$, $t$, $u$, $v$, and $w$ be the trisection points of the sides of $abcd$, as shown. [asy] unitsize(1 cm); pair a, b, c, d, p, q, r, s, t, u, v, w; a = (1,2); b = (4,3); c = (5,-1); d = (0,0); p = (2*a + b)/3; q = (a + 2*b)/3; r = (2*b + c)/3; s = (b + 2*c)/3; t = (2*c + d)/3; u = (c + 2*d)/3; v = (2*d + a)/3; w = (d + 2*a)/3; fill(a--q--r--c--u--v--cycle, gray(0.7)); draw(a--b--c--d--cycle); draw(q--r); draw(u--v); dot("$a$", a, nw); dot("$b$", b, ne); dot("$c$", c, se); dot("$d$", d, sw); dot("$p$", p, n); dot("$q$", q, n); dot("$r$", r, e); dot("$s$", s, e); dot("$t$", t, dir(270)); dot("$u$", u, dir(270)); dot("$v$", v, nw); dot("$w$", w, nw); [/asy] if the area of quadrilateral $abcd$ is 180, then find the area of hexagon $aqrcuv$.