The three medians of a triangle measure 9 cm, 12 cm and 15 cm. What is the area of the triangle?

A triangle built from the three medians has $\frac{3}{4}$ of the area of the original. The medians 9, 12, 15 form a right triangle of area $\frac{1}{2}\times 9\times 12=54{\text{cm}}^2$, so the original area is $\frac{4}{3}\times 54=72{\text{cm}}^2$.