A 3×10, rectangle sits inside a circle with radius of 12. What is the area of the shaded region? Round your final answer to the nearest hundredth.

 The area of the circle for this case is given by:
 [tex]A1 = \pi * r ^ 2 [/tex]Where,
 r: radius of the circle.
 Substituting values we have:
 [tex]A1 = \pi * (12) ^ 2 A1 = 452.3893421[/tex]
 The area of the rectangle is given by:
 [tex] A2 = (w) * (l) [/tex]
 Where,
 w: width
 l: long
 Substituting values we have:
 [tex]A2 = (3) * (10) A2 = 30[/tex]
 The area of the shaded region is:
 [tex]A1 - A2 = 452.3893421 - 30 A1 - A2 = 422.3893421[/tex]
 Rounding off we have:
 [tex]A1 - A2 = 422.39 [/tex]
 Answer:
 The area of the shaded region is:
 A1 - A2 = 422.39