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?
Question 6 options:
272
374
102
59
To find the area in square feet of the part of the backyard in which Shayne is allowed to dig, we need to subtract the area of the rectangle around the utility line from the total area of the backyard.
The total area of the backyard is given as 272 square feet (width = 17 feet, length = 16 feet).
The utility line has a width of 3 feet, so the rectangle around the utility line will have a width of 3 + 3 = 6 feet (subtracting 3 feet on each side of the utility line).
The length of the rectangle around the utility line will be the same as the length of the backyard, which is 16 feet.
Therefore, the area of the rectangle around the utility line is 6 feet * 16 feet = 96 square feet.
Finally, to find the area in square feet of the part of the backyard in which Shayne is allowed to dig, we subtract the area of the rectangle around the utility line from the total area of the backyard:
272 square feet - 96 square feet = 176 square feet
Therefore, the area in square feet of the part of the backyard in which Shayne is allowed to dig is 176.
So the correct answer is 176.