Calculate Triangle Area: Using 1/4 Side Ratio and Height of 12

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

• Step 1: Calculate the length of side BC using the given ratio to AE.
• Step 2: Use the formula for the area of a triangle with the calculated BC and given AE.

Let's work through these steps:

Step 1: Calculate BC
Given that BC is $\frac{1}{4}$ the length of AE, and AE is 12, we find the length of BC as follows:

$BC = \frac{1}{4} \times 12 = 3$

Step 2: Use the formula for the area of a triangle
The formula is given by $A = \frac{1}{2} \times \text{base} \times \text{height}$.

In this context, BC serves as the base, and AE serves as the height. Thus, we compute the area:

$A = \frac{1}{2} \times BC \times AE = \frac{1}{2} \times 3 \times 12 = \frac{1}{2} \times 36 = 18$

Therefore, the area of triangle $\triangle$ ABC is $\mathbf{18}$.

Thus, the correct answer is choice 4: $\mathbf{18}$.