The area of the section of the lawn that is not watered by either sprinkler is 139.06 feet².
How do we find the area not watered by the sprinkler?
The lawn measures 18' by 36', the total area is:
Total area = 18 × 36
Total area = 648
Each sprinkler covers a quarter circle with a radius of 18 feet because they only spray in a 90-degree (or quarter) sector.
The area of a full circle is πr², so the area covered by each sprinkler is a quarter of that:
Area covered by one sprinkler = πr²/4
Area_not watered = Area_lawn − 2 ×( 1/4πr²)
Area_not watered = 648 − 2 ×( 1/4πr²)
(1/4)π(324) = 254.469
2 × 254.469 = 508.938
Area_not watered = 648 - 508.938
Area_not watered = 139.062
The area of the section of the lawn that is not watered by either sprinkler is approximately 139.06 square feet.