A utility line runs underground through Shayne’s rectangular backyard. Shayne is not allowed to dig within 3 feet of the utility line. The diagram below shows the dimensions of Shayne’s backyard in feet. The dashed line represents the utility line.What is the area in square feet of the part of the backyard in which Shayne is allowed to dig?
No diagram shown.
To find the area in square feet of the part of the backyard in which Shayne is allowed to dig, follow these steps:
1. Determine the dimensions of Shayne's backyard: Look at the given diagram to find the measurements of the length and width of the rectangular backyard. Let's say the length is L feet and the width is W feet.
2. Calculate the area of the entire backyard: To find the total area, multiply the length with the width. The formula for the area of a rectangle is A = L * W.
3. Determine the area that needs to be excluded: Since Shayne is not allowed to dig within 3 feet of the utility line, subtract 3 feet from each side of the rectangle. This will create a smaller rectangle within the backyard where digging is permitted.
4. Calculate the area of the excluded part: To find the area of the excluded part, multiply the new length and width of the smaller rectangle. Let's call the updated length L' and the updated width W'. So, the area of the excluded part is given by A_excluded = (L - 2*3) * (W - 2*3).
5. Calculate the area of the allowed part: The area of the allowed part is equal to the total area of the backyard minus the area of the excluded part. So, the area of the allowed part is given by A_allowed = A - A_excluded.
6. Get the final answer: Substitute the values into the formula and calculate the area of the allowed part.
By following these steps, you can find the area in square feet of the part of the backyard in which Shayne is allowed to dig.