Step-by-Step Solution
Key Concept: Find intersection points by substitution, then use the distance formula or coordinate geometry to calculate the area of the resulting triangle.
Substituting $y = x^2$ into $x^2 + (y - 2)^2 = 8$, we get $y + (y-2)^2 = 8$, which simplifies to $y^2 - 3y - 4 = 0$ or $y = -1, 4$. For $y = 4$: $x^2 = 4 \Rightarrow x = \pm 2$ (otherwise $x$ is not defined). For $y = -1$: $x^2 = -1$ is impossible. Let $B = (-2,4)$ and $C = (2,4)$. The area of $\triangle OBC = \frac{1}{2} \times 4 \times 4 = 8$ square units.
Correct Answer: 8