27.

27

In any convex polygon, you can count the number of diagonals as follows.

From each of the N vertices, you can draw a diagonal to the (N-3) non-adjacent vertices. Doing so, you will draw each diagonal twice. Thus, there are

9(9-3)/2 = 9*6/2 =

From each of the N vertices, you can draw a diagonal to the (N-3) non-adjacent vertices. Doing so, you will draw each diagonal twice. Thus, there are

**n(n-3)/2 diagonals**in an n-sided shape.9(9-3)/2 = 9*6/2 =

**27 diagonals**