The diagram shows a square-based pyramid with base $P Q R S$ and vertex $O$. All the edges of the pyramid are of length 20 metres.
Find the shortest distance, in metres, along the outer surface of the pyramid from $P$ to the midpoint of $O R$.
A $10 \sqrt { 5 - 2 \sqrt { 3 } }$
B $10 \sqrt { 3 }$
C $10 \sqrt { 5 }$
D $10 \sqrt { 7 }$
E $10 \sqrt { 5 + 2 \sqrt { 3 } }$