An important ambiguity is exactly what, in "from center of tile to outside is 13 cm", "outside" refers to. Do you mean the center of an ouside edge or a vertex? A regular hexagon can be divided into 6 equilateral triangles by drawing lines from the center of the hexagon to the six vertices.
If the "13 cm" is from the center of the hexagon to a vertex, then the "base" of each triangle has length 13 while the "altitude" has length \(\displaystyle 13\frac{\sqrt{3}}{2}\). Since the area of a triangle is "1/2 height times base", the area of each of the six equilateral triangles making up the hexagon is \(\displaystyle 169\frac{\sqrt{3}}{4}\).
If, instead, the "13 cm" is from the center of the hexagon to the center of a side, then the "base" of each triangle has length \(\displaystyle \frac{2\sqrt{3}}{2}s\) while the altitude has length 13. The area or each triangle, in this case, is \(\displaystyle 169\frac{\sqrt{3}}{3}\).
The area of the hexagon is, of course, 6 times the area of each triangle and the volume of a prizm is the area of the base times the height of the prizm.
