27.
How Many Diagonals Does A 9 Sided Shape Have ?
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 n(n-3)/2 diagonals in an n-sided shape.
9(9-3)/2 = 9*6/2 = 27 diagonals
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