The Area of the Surface $\mathbf { r } ( u , v ) = u \mathbf { i } - \frac { v } { 2 } \mathbf { j } + \frac { v } { 2 } \mathbf { k }$

Multiple Choice

The area of the surface $\mathbf { r } ( u , v ) = u \mathbf { i } - \frac { v } { 2 } \mathbf { j } + \frac { v } { 2 } \mathbf { k }$ , where $0 \leq u \leq 2,0 \leq v \leq 1$ is

A) $5 \sqrt { 2 }$
B) $4 \sqrt { 2 }$
C) $3 \sqrt { 2 }$
D) $2 \sqrt { 2 }$
E) $\sqrt { 2 }$