As shown in the figure, there is a cube $\mathrm { ABCD } - \mathrm { EFGH }$ with edge length 4. Let M be the midpoint of segment AD. What is the area of triangle MEG? [3 points]\\
(1) $\frac { 21 } { 2 }$\\
(2) 11\\
(3) $\frac { 23 } { 2 }$\\
(4) 12\\
(5) $\frac { 25 } { 2 }$