area of circular sector

Problem
A 30° right triangular lot has the long leg measuring 67 m. On the long leg and 15 m from the short leg, is a peg to which a goat is tied such that the farthest distance its mouth can reach is 30 m from the peg. Find the area inside the lot from which the goat can graze.
 

Problem
A circular sector of radius 10 cm is inscribed in a square of sides 10 cm such that the center of the circle is at the midpoint of one side of the square. Find the area of the sector in cm².