6. (10 points) As shown in the figure, the area of $\triangle A B C$ is 100 square centimeters, and the area of $\triangle A B D$ is 72 square centimeters. $M$ is the midpoint of side $C D$, $\angle M H B=90^{\circ}$, and it is known that $A B=20$ centimeters. Then the length of $M H$ is $\qquad$ centimeters.
【Analysis】We can use the area formula to find the heights of $\triangle A B C$ and $\triangle A B D$ respectively, and given $A B=20$ cm, we can use the midline property of $M H$ to find the length of $M H$.

【Solution】Solution: According to the analysis, draw $D E \perp A B$ intersecting $A B$ at $E$, and $C F \perp A B$ intersecting $A B$ at $F$, as shown in the figure:
The area of $\triangle A B D = 72 = \frac{1}{2} \times \mathrm{DE} \times \mathrm{AB} = \frac{1}{2} \times \mathrm{DE} \times 20, \therefore D E = 7.2$ cm,
The area of $\triangle A B C = 100 = \frac{1}{2} \times \mathrm{CF} \times \mathrm{AB} = \frac{1}{2} \times \mathrm{CF} \times 20, \therefore C F = 10$ cm;
Also, since $M H = \frac{1}{2} \times (\mathrm{DE} + \mathrm{CF}) = \frac{1}{2} \times (7.2 + 10) = 8.6$ cm.
Therefore, the answer is: 8.6.