SOLUTION: A circle surrounds a rectangle. A rectangle is 12 feet long and 9 feet high. The circle touches all four corners of the rectangle. what is the size of the shaded area(the left over

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Question 273717: A circle surrounds a rectangle. A rectangle is 12 feet long and 9 feet high. The circle touches all four corners of the rectangle. what is the size of the shaded area(the left over circle).
Answer by CharlesG2(834) About Me  (Show Source):
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A circle surrounds a rectangle. A rectangle is 12 feet long and 9 feet high. The circle touches all four corners of the rectangle. what is the size of the shaded area(the left over circle).
area of rectangle = length * width = 12 * 9 = 108
area of circle = pi * radius^2 (need to find radius)
center of rectangle should be the center of the circle
so we should have a right triangle with legs of 4.5 and 6, the hypotenuse of this triangle should be the radius of the circle
4.5^2 + 6^2 = radius^2
20.25 + 36 = 56.25
area of shaded area (left over circle) = 56.25pi - 108
176.714587 - 108
68.714587 or approx 68.7 ft^2 is the shaded area