A sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet. What is the area of the circular region covered by the sprinkler? Express your answer to the nearest square foot.

Answer: The area covered by the sprinkler is 452 square feet

Step-by-step explanation: If the sprinkler rotates around in a circular motion, then the sprinkler's length is a radius (since it moves in a complete circle while rooted to one spot). Having derived the radius as 12 feet, the area of the region covered by the sprinkler can be calculated as

Area of a circle = pi x radius^2

Area of a circle = 3.14 x 12^2

Area of a circle = 3.14 x 144

Area of a circle = 452.16

Therefore, the area of the region covered by the sprinkler is approximately 452 square feet