$\triangle PQR$ has an area of $27\,\text{cm}^2$ and a base measuring $6$ cm. What is the height, $h,$ of $\triangle PQR?$ [asy]
draw((0,0)--(6,0)--(4,9)--cycle);
draw((4,.5)--(4.5,.5)--(4.5,0));
draw((4,9)--(4,0));
label("$h$",(4,4.5),E);
label("$Q$",(0,0),W);
label("$R$",(6,0),E);
label("$P$",(4,9),N);
label("6 cm",(3,0),S);
[/asy]
The area of a triangle can be calculated using the formula $\mbox{Area}=\frac{1}{2}\times \mbox{base} \times \mbox{height}.$

The area is $27\,\text{cm}^2$ and the base measures $6\,\text{cm}.$ Substituting these values into the formula, $$A=\frac{1}{2}\times b \times h$$becomes $$27=\frac{1}{2} \times 6 \times h$$or $27=3h.$ Therefore, $h=\boxed{9}\,\text{cm}.$