Find the Area of the Portion of the Surface $f ( x , y ) = 7 + \frac { 2 } { 3 } y ^ { \frac { 3 } { 2 } }$

Multiple Choice

Find the area of the portion of the surface $f ( x , y ) = 7 + \frac { 2 } { 3 } y ^ { \frac { 3 } { 2 } }$
that lies above the region $R = \{ ( x , y ) : 0 \leq x \leq 4,0 \leq y \leq 4 - x \}$ . Round your answer to two decimal places.

A) $0.05$
B) $2.18$
C) $11.97$
D) $1.22$
E) $12.51$