To calculate the uncertainty of the surface area for the given box, we first need to understand the formula for the surface area of a rectangular box:

$A = 2lw + 2lh + 2wh$

Where:

• $l$ is the length
• $w$ is the width
• $h$ is the height (we do not have this information, but we assume it is the same as the width in this case)

The uncertainty of the surface area can be calculated using error propagation formulas. Given the uncertainties for length and width are $\pm 2 \, \text{cm}$ and $\pm 2 \, \text{cm}$ respectively, the uncertainty in the surface area $\Delta A$ can be approximated by:

$\Delta A = \left( \frac{\partial A}{\partial l} \Delta l \right) + \left( \frac{\partial A}{\partial w} \Delta w \right)$

Where the partial derivatives are:

$\frac{\partial A}{\partial l} = 2w + 2h$ $\frac{\partial A}{\partial w} = 2l + 2h$

We need to compute the values for the surface area based on the given dimensions and uncertainties.

I'll walk you through the necessary calculations. Would you like to proceed?