To find the lateral surface area of a rectangular prism, we use the formula:
\[ \text{Lateral Surface Area} = 2h(l + w) \]
where \( h \) is the height, \( l \) is the length, and \( w \) is the width.
Given:
- \( h = 2 , \text{cm} \)
- \( l = 4 , \text{cm} \)
- \( w = 5 , \text{cm} \)
Now, substitute the values into the formula:
\[ \text{Lateral Surface Area} = 2 \times 2 \times (4 + 5) \]
Calculating inside the parentheses first:
\[ 4 + 5 = 9 \]
Now substituting back in:
\[ \text{Lateral Surface Area} = 2 \times 2 \times 9 = 4 \times 9 = 36 , \text{cm}^2 \]
Thus, the lateral surface area of the rectangular prism is:
\[ \boxed{36 , \text{cm}^2} \]