Calculate Parallelogram Height AE: Given Area 82 cm² and Base 4 cm

To solve for AE in a parallelogram ABCD where DC serves as the base, follow these steps:

• Step 1: Identify the given data. The base DC is 4 cm, and the area of the parallelogram is 82 cm².
• Step 2: Recall the area formula for a parallelogram: $\text{Area} = \text{base} \times \text{height}$.

Now, we begin the calculation:
- The base DC is 4 cm, so we have: $82 = 4 \times \text{AE}$.
- Solving for AE: $\text{AE} = \frac{82}{4}$.

Dividing 82 by 4 yields:
- $\text{AE} = 20.5$ cm.

Therefore, the length of AE is $\boxed{20.5}$ cm, aligning with choice 3.