Calculate Length DF in Parallelogram ABCD: Given AB=12cm, ED=8cm, BC=10cm

To solve for the length of $DF$, let's consider both ways of calculating the area of parallelogram $ABCD$:

• Step 1: Calculate area using base $AB$:
  $\text{Area} = AB \times ED = 12 \times 8 = 96$ square cm.
• Step 2: Calculate area using base $BC$:
  $\text{Area} = BC \times DF = 10 \times DF$.
• Equate 96 to $10 \times DF$:
  $10 \times DF = 96$.
• Step 3: Solve for $DF$ by dividing by 10:
  $DF = \frac{96}{10} = 9.6$ cm.

Therefore, the length of $DF$ is $9.6$ cm.

Hence, the correct answer is choice 4, which is $9.6$ cm.