Calculate Triangle Area with 1/5 Ratio: Height-Base Geometry Problem

To solve the problem, we will follow these steps:

• Step 1: Using $AE = 10$, calculate $BC$ using the information that $BC = \frac{1}{5} \times AE$.
• Step 2: Apply the formula for the area of a triangle.

We proceed with the calculations:
Step 1: Since $BC = \frac{1}{5} \times 10 = 2$.
Step 2: Assume $AB$ is perpendicular to $BC$ to apply the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

The triangle $\triangle ABC$ is vertical, implying that base $BC$ and height $AE$ can be used because it suggests $AE$ is perpendicular to $BC$. Thus,
$\text{Area} = \frac{1}{2} \times AE \times BC = \frac{1}{2} \times 10 \times 2 = 10$.

Therefore, the area of the triangle is $10$.