SOLUTION: A circular rock garden with a diameter of 50 feet is placed in the middle of a square grass yard. If the perimeter of the yard is 108 yards, then how much area is covered by grass?

Question 1159567: A circular rock garden with a diameter of 50 feet is placed in the middle of a square grass yard. If the perimeter of the yard is 108 yards, then how much area is covered by grass?
For all calculations involving π, use π ≈ 3.14.
Hint: Be careful that you do not do any rounding on answers until the very end of a problem part, or you could create rounding error.
a) Amount of area covered by grass, measured in square feet = _____ square feet.
DO NOT TYPE COMMAS. Round your answer to 2 decimal places as needed.
b) Amount of area covered by grass, measured in square yards = _____ square yards.
Round your answer to 2 decimal places as needed
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

To find the area of a square given the perimeter, divide the perimeter by 4 and square the result. To find the area of a circle given the diameter, divide the diameter by 2, square the result and then multiply by

. At this point, you can either divide the area of the circle by 27 to get the area of the circle in square yards, or multiply the area of the square by 27 to get the are of the square in square feet. Converting the circle to square yards has the disadvantage of introducing a rounding error that compounds when using the result in a subsequent computation, whereas converting the square to square feet has the disadvantage of having to divide your final answer by 27 to convert the answer to the requested square yards. Either way, you have to subtract the area of the circle from the area of the square once they are expressed in the same units.

John

My calculator said it, I believe it, that settles it

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