Let a = 30! , b = 50! , and c = 100! . Consider the following numbers:

log_a c, log_c a, log_b a, log_a b

Which one of the following inequalities is CORRECT?

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown.

The area of the shaded region is __________ cm².