To find the height of the rectangular ink pad, you can use the formula for the area of a rectangle:
\[ \text{Area} = \text{width} \times \text{height} \]
Given that the area is 130 square centimeters and the width is 13 centimeters, you can set up the equation:
\[ 130 = 13 \times \text{height} \]
To find the height, divide both sides of the equation by 13:
\[ \text{height} = \frac{130}{13} \]
Calculating the right side gives:
\[ \text{height} = 10 \]
Thus, the height of the ink pad is
\[ \boxed{10} \text{ centimeters}. \]