If in triangle $ABC$ , $AC$=$15$, $BC$=$13$ and $IG||AB$ where $I$ is the incentre and $G$ is the centroid , what is the area of triangle $ABC$ ?
1. **Identify the given information and the goal:**
   - In triangle $ABC$, we have $AC = 15$, $BC = 13$, and $IG \parallel AB$ where $I$ is the incenter and $G$ is the centroid.
   - We need to find the area of triangle $ABC$.

2. **Extend $CI$ and $CG$ to meet $AB$ at points $D$ and $M$ respectively:**
   - $M$ is the midpoint of $AB$ because $G$ is the centroid, and the centroid divides the median in the ratio $2:1$.

3. **Use the given parallel condition $IG \parallel DM$:**
   - Since $IG \parallel DM$, we have $\frac{CI}{ID} = \frac{CG}{GM}$.

4. **Use the known ratios:**
   - It is well known that $\frac{CG}{GM} = 2$ (since the centroid divides the median in the ratio $2:1$).
   - By the Angle Bisector Theorem, $\frac{CI}{ID} = \frac{a+b}{c}$ where $a = BC$, $b = AC$, and $c = AB$.

5. **Set up the equation using the ratios:**
   - Given $\frac{CI}{ID} = \frac{a+b}{c}$ and $\frac{CG}{GM} = 2$, we equate them:
     \[
     \frac{a+b}{c} = 2
     \]
   - Substitute $a = 13$ and $b = 15$:
     \[
     \frac{13 + 15}{c} = 2
     \]
     \[
     \frac{28}{c} = 2
     \]
     \[
     c = \frac{28}{2} = 14
     \]

6. **Determine the area of triangle $ABC$:**
   - We now have the side lengths $a = 13$, $b = 15$, and $c = 14$.
   - The area of a triangle with sides $13$, $14$, and $15$ is known to be $84$ square units (this can be verified using Heron's formula).

The final answer is $\boxed{84}$.