Triangle Area Calculation: Using 1/3 Ratio and 6-Unit Height

Let's calculate the area of triangle ABC by following these steps:

• Step 1: Calculate AE using the ratio. Given that side BC is $\frac{1}{3}$ of AE, if we call AE = 6 (as shown or suggested by the illustration, considering AE is the vertical height), then $BC = \frac{1}{3} \times 6 = 2$.
• Step 2: The height of triangle ABC is given by the length AE, which is 6.
• Step 3: Calculate the area using the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times BC \times AE = \frac{1}{2} \times 2 \times 6 = 6$.

Therefore, the area of triangle ABC is $\text{6}$.