Trapezoid Area Problem: Finding Side Length Given Area = 12cm²

The problem requires finding the height of a trapezoid given its area and the lengths of its bases. We'll use the trapezoid area formula to do this:

• The formula for the area of a trapezoid is $A = \frac{1}{2} \times (b_1 + b_2) \times h$.
• Substituting in the known values: $12 = \frac{1}{2} \times (5 + 7) \times h$.
• Simplify: $12 = \frac{1}{2} \times 12 \times h$.
• Further simplification gives: $12 = 6 \times h$.
• Solving for $h$, we divide both sides by 6: $h = \frac{12}{6}$.
• Thus, $h = 2$ cm.

By comparing this result to the answer choices, we see that the correct answer is $2 \, \text{cm}$.

Therefore, the length of the side marked in red is $\textbf{2 cm}$.