The Surface Area of the Surface in the First Octant $x ^ { 2 } + y ^ { 2 } = z ^ { 2 }$

Multiple Choice

The surface area of the surface in the first octant cut from $x ^ { 2 } + y ^ { 2 } = z ^ { 2 }$ by x + y = 4 is

A) $6 \sqrt { 3 }$
B) $4 \sqrt { 6 }$
C) $6 \sqrt { 2 }$
D) $8 \sqrt { 2 }$
E) 9