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 116 yards, then how much area is covered by grass?
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Question 1148756: 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 116 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 = Blank
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 = Blank
square yards.
Round your answer to 2 decimal places as needed
The perimeter of the square is 116 yards = 348 feet; so the side of the square is 348/4 = 87 feet. The area of the whole yard is then 87^2 = 7569 square feet.
The rock garden has a diameter of 50 feet, so a radius of 25 feet. The area of the rock garden in square feet is then .
The area of the grass is the area of the whole garden, minus the area of the rock garden.
Do the calculations in square feet as directed; the area is square yards is the area in square feet divided by 9 (the number of square feet in a square yard).
