Find the Area of the Part of the Cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$

Multiple Choice

Find the area of the part of the cone $4 x ^ { 2 } + 4 y ^ { 2 } = z ^ { 2 }$ that is above the region in the first quadrant bounded by the line y = x and the parabola $y = x ^ { 2 }$ .

A) $\frac { 5 } { 6 }$

B) $\frac { 5 } { 3 }$
C) $\frac { 2 } { 3 }$
D) 2
E) $\frac { \sqrt { 5 } } { 6 }$
F) $\frac { \sqrt { 5 } } { 3 }$

G) $\frac { \sqrt { 2 } } { 5 }$
H) 6