Transcript:
The diagram shows a square based pyramid with base PQRS and vertex O. All the edges are length 20 meters. Find the shortest distance, in meters, along the outer surface of the pyramid from P to the midpoint of OR.
The only way I have been able to solve this question is using a computer and the paper is non calculator, so there must be a faster, better solution.
My solution is creating a point X on OQ and labelling the midpoint of OR as M, and setting $\theta = OPQ$. I then calculated $PX + PM$ in terms of $\theta$ and found the minimum point of this function, in order to find the shortest possible distance. Finding the minimum point would be nowhere near possible under time constraint without a computer.
I have included the correct answer, so it is the working I am looking for.
Answer:
D $10\sqrt7$
Best Answer
Hint:
The distance has to be a straight line along the net of the pyramid. There are two options:
The first line has lenght $10\sqrt{7+2\sqrt{3}}$, and the second one has $10\sqrt{7}$, which is the smaller one.