If L is the mid-point of the side YZ of XYZ, and the area of XYL is 13 cm², then the area (in cm²) of XYZ is _____.

The correct option is 26.

To find the area of triangle XYZ, let us analyze the geometric properties given in the problem statement.

1. We are given a triangle XYZ where L is the midpoint of the side YZ.
2. A line segment joining a vertex of a triangle to the midpoint of the opposite side is called a median. Therefore, the segment XL is the median of triangle XYZ drawn from vertex X to the side YZ.

3. An important geometric property of triangles states that a median divides a triangle into two smaller triangles of equal area.

Thus, the median XL divides triangle XYZ into two equal-area triangles: triangle XYL and triangle XZL.

$\text{Area of}\mathrm{\Delta }\text{XYL}=\text{Area of}\mathrm{\Delta }\text{XZL}$

4. The total area of triangle XYZ is the sum of the areas of these two smaller triangles:

$\text{Area of}\mathrm{\Delta }\text{XYZ}=\text{Area of}\mathrm{\Delta }\text{XYL}+\text{Area of}\mathrm{\Delta }\text{XZL}$

$\text{Area of}\mathrm{\Delta }\text{XYZ}=2\times \text{Area of}\mathrm{\Delta }\text{XYL}$

5. Given that the area of triangle XYL is 13 cm², we substitute this value into the equation:

$\text{Area of}\mathrm{\Delta }\text{XYZ}=2\times 13{\text{cm}}^2=26{\text{cm}}^2$

Therefore, the area of triangle XYZ is 26 cm².