Triangle Area Calculation: Using Median AD to Find Area of Triangle ABC from Area 15

To solve this problem, we'll employ the theorem which states that the median of a triangle divides it into two triangles of equal area. Given that $AD$ is a median of $\triangle ABC$, it divides $\triangle ABC$ into $\triangle ADB$ and $\triangle ADC$.

Step 1: Recognize the properties of a median. The median $AD$ implies:
- Area of $\triangle ADB =$ Area of $\triangle ADC$.
- Given Area of $\triangle ADB = 15$, hence Area of $\triangle ADC = 15$.

Step 2: Compute the total area of $\triangle ABC$:
- Total Area of $\triangle ABC =$ Area of $\triangle ADB +$ Area of $\triangle ADC = 15 + 15 = 30.$

Thus, the area of triangle $\triangle ABC$ is $\boxed{30}$.