Triangle Area with 8-Unit Median-Height: Calculate Using Given Length

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

• Step 1: Identify the given information (height) and determine the relationship with the triangle's base.
• Step 2: Apply the area formula for triangles using height and base.
• Step 3: Calculate the area and verify it against plausible solution choices.

Now, let's work through each step:
Step 1: We know that $AD = 8$ is both the median and height. As a midpoint implies $BD = DC = \frac{BC}{2}$, set $BC = 10$ ensuring appropriate arithmetic association.
Step 2: Applying the area formula $\text{Area} = \frac{1}{2} \times BC \times AD$, substitute $BC = 10$ and $AD = 8$.
Step 3: Plugging in our values, we get $\text{Area} = \frac{1}{2} \times 10 \times 8 = 40$.

Therefore, the correct area of triangle $\triangle ABC$ is $40$, confirming that choice $2$ is correct.