Parabola

Step 1: Equation of the parabola.
The equation of the parabola is . The latus rectum of a parabola is the line segment passing through the focus and perpendicular to the axis of symmetry. For a parabola of the form , the length of the latus rectum is . For , we have , so the length of the latus rectum is 8 units.
Step 2: Find the area.
The area of the region bounded by the parabola and its latus rectum can be calculated by integrating the equation of the parabola from 0 to 8. The equation of the parabola gives . Therefore, the area is given by: Simplifying the integral, we get:
Step 3: Conclusion.
Thus, the area of the region is sq. units, which corresponds to option (C).