1. **State the problem:** Calculate the area of the shaded part inside triangle ABC where M is the intersection of the medians. 2. **Recall the property of medians:** The medians of a triangle intersect at the centroid M, which divides each median in a ratio 2:1. 3. **Area relation:** The shaded part formed by the intersection of the medians is the smaller triangle formed inside ABC. This smaller triangle has an area exactly $\frac{1}{4}$ of the original triangle ABC. 4. Given, area of $\triangle ABC = 36$ cm$^2$. 5. Therefore, area of the shaded part = $\frac{1}{4} \times 36 = 9$ cm$^2$. **Final answer:** The area of the shaded part is 9 cm$^2$.