An Isosceles triangle is inscribed in a semicircle, as shown in the diagram, and it continues to be inscribed as the semicircle changes size. The area of the semicircle is increasing at the rate of 1 cm^2/sec when the radius of the semicircle is 3 cm.
a) How fast is the radius of the semicircle increasing when the radius is 3 cm? Include units in your answer
b) How fast is the perimeter of the semicircle increasing when the radius is 3 cm? Include units in your answer
c) How fast is the area of the isosceles triangle increasing when the radius is 3 cm? Include units in your answer.
d) How fast is the shaded region increasing when the radius is 3 cm? Include units in your answer.