Find the Missing Side AD in a Trapezoid with 42cm Perimeter

To solve this problem, we'll follow these steps:

• Step 1: Identify the given perimeter and side lengths.
• Step 2: Use the perimeter formula for a trapezoid.
• Step 3: Solve for the missing side $AD$.

Let's begin:

Step 1: We know that the perimeter $P = 42$ cm. The other sides are $AB = 14$ cm, $BC = 7$ cm, and $CD = 12$ cm.

Step 2: The formula for the perimeter is:

$P = AB + BC + CD + AD$

Substituting in the known values:

$42 = 14 + 7 + 12 + AD$

Step 3: Simplify the equation to find $AD$:

$42 = 33 + AD$

Subtract 33 from both sides:

$AD = 42 - 33$

$AD = 9$

Therefore, the length of side $AD$ is $\textbf{9 cm}$.