Suppose that $P Q$ and $R S$ are two chords of a circle intersecting at a point $O$. It is given that $P O = 3 \mathrm {~cm}$ and $S O = 4 \mathrm {~cm}$. Moreover, the area of the triangle $P O R$ is $7 \mathrm {~cm} ^ { 2 }$. Find the area of the triangle $Q O S$.