c. \(312 \space \text { cm} ^ 2\)

Given:

- Length (\(l\)) = 12 cm

- Width (\(w\)) = 8 cm

- Height (\(h\)) = 3 cm

The surface area (\(SA\)) of a rectangular prism is given by:

\(SA = 2lw + 2lh + 2wh\)

Let's calculate each term separately:

1. Calculate \(2lw\):

\(2lw = 2 \times 12 \times 8 = 2 \times 96 = 192 \space \text { cm} ^ 2\)

2. Calculate \(2lh\):

\(2lh = 2 \times 12 \times 3 = 2 \times 36 = 72 \space \text { cm} ^ 2\)

3. Calculate \(2wh\):

\(2wh = 2 \times 8 \times 3 = 2 \times 24 = 48 \space \text { cm} ^ 2\)

Now, sum these areas to find the total surface area:

\(SA = 192 + 72 + 48 = 312 \space \text { cm} ^ 2\)

Supplemental Knowledge

The surface area of a rectangular prism (also known as a cuboid) is calculated by finding the sum of the areas of all six rectangular faces. The formula for the surface area of a rectangular prism with length \(l\), width \(w\), and height \(h\) is:

\[SA = 2lw + 2lh + 2wh\]

This formula accounts for each pair of opposite faces on the prism.