Problem $4$: $(15$ points$)$

The thrust of the Space Shuttle main engine $($SSME$)$ at $100\%$ power level had a thrust of $1\mathrm{.}817{10}^{6}N$ at sea level, and $2\mathrm{.}278{10}^{6}N$ in vacuum. Use this information to determine the nozzle exit area $A_e.$