Centroids of Seven Triangles in an Octagon

An octagon $ABCDEFGH$ is obtained from a $23 \times 27$ rectangle by cutting off a right triangle with side lengths $6$, $8$, $10$ from each corner, so that $AB = CD = EF = GH = 10$ and $BC = DE = FG = HA = 11$, as shown in the figure. Let $J$ be the midpoint of $HA$. The segments $JB$, $JC$, $JD$, $JE$, $JF$, $JG$ divide the octagon into $7$ triangles. Find the area of the convex polygon whose vertices are the centroids of these $7$ triangles.