The area of the shaded region is the quarter circle minus the isosceles right triangle. The area of quarter-circle is pi*r^2/4=pi*8^2/4=16pi. The area of triangle is 8*8/2=32, so the area is 16pi-32.
The perimeter of the shaded region is the length of arc plus the segment. The length of arc is pi*2r/4=pi*16/4=4pi, and the length of the segment is 8*\sqrt(2) according to pythagorean's theorem. The total perimeter is 4pi+8*\sqrt(2).
