Calculate Line Segment AF in Parallelogram ABCD with Given Measurements

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

• Step 1: Identify the given dimensions and properties of parallelogram $ABCD$.
• Step 2: Calculate the area of the parallelogram using the known base and height.
• Step 3: Use the area and other dimensions to determine the required segment $AF$.

Now, let's work through each step:

Step 1: Parallelogram $ABCD$ has $AB = 6$ cm and $AD = 4$ cm. The height from $B$ opposite $AD$ is $3$ cm.

Step 2: Calculate the area with base $AB$:

$\text{Area} = 6 \times 3 = 18$ square centimeters.

Step 3: Use base $AD$ to find $AF$ (height):

$18 = 4 \times AF$.

Solve for $AF$:

$AF = \frac{18}{4} = 4.5$ cm.

Therefore, the solution to the problem is $AF = 4.5$ cm.