Triangle Area with 5/8 Ratio: Calculate Using 16-Unit Height

To solve this problem, let's proceed step-by-step:

Step 1: Calculate the length of $BC$
Given $BC = \frac{5}{8} \times AE$ and $AE = 16$, calculate:

$BC = \frac{5}{8} \times 16 = \frac{80}{8} = 10$

Step 2: Use the triangle area formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.
Substitute $BC = 10$ as the base and $AE = 16$ as the height:

$\text{Area} = \frac{1}{2} \times 10 \times 16$

Step 3: Perform the calculation:

$\text{Area} = \frac{1}{2} \times 160 = 80$

Therefore, the area of triangle $\triangle ABC$ is $\boxed{80}$.