If $L$ is the mid-point of the side $YZ$ of $△XYZ$, and the area of $△XYL$ is $13{\text{cm}}^2$, then the area (in ${\text{cm}}^2$) of $△XYZ$ is:

In $△XYZ$, since $L$ is the mid-point of side $YZ$, the line segment $XL$ forms a median of the triangle from vertex $X$.
A fundamental property of geometry states that a median divides a triangle into two smaller triangles of equal area. Therefore:

$$\text{Area}(△XYL)=\text{Area}(△XZL)=13{\text{cm}}^2$$

The total area of $△XYZ$ is the sum of the areas of these two smaller triangles:

$$\text{Area}(△XYZ)=2\times \text{Area}(△XYL)$$

$$\text{Area}(△XYZ)=2\times 13=26{\text{cm}}^2$$