A rectangular yard measuring 36 ft by 51 ft is bordered (and surrounded) by a fence. Inside, a walk that is 4 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
To find the area of the walk, we need to subtract the area of the yard from the area of the yard including the walk.
The area of the yard is 36 ft x 51 ft = 1836 sq ft.
The yard including the walk is 44 ft x 59 ft (36 ft + 2 * 4 ft for the width and 51 ft + 2 * 4 ft for the length) = 2596 sq ft.
Therefore, the area of the walk is 2596 sq ft - 1836 sq ft = <<2596-1836=760>>760 sq ft. Answer: \boxed{760\text{ sq ft}}.
To find the area of the walk, we need to subtract the area of the yard from the area of the larger rectangle formed by the border of the walk.
The larger rectangle is formed by adding twice the width of the walk (4 ft on each side) to the length and width of the yard.
So, the length of the larger rectangle is (36ft + 2(4ft)) = 44ft and the width is (51ft + 2(4ft)) = 59ft.
Now, we can find the area of the larger rectangle by multiplying its length and width:
Area of the larger rectangle = length * width = 44ft * 59ft = 2596 sq ft.
Next, we need to find the area of the yard, which is simply the length times the width:
Area of the yard = 36ft * 51ft = 1836 sq ft.
Finally, we subtract the area of the yard from the area of the larger rectangle to get the area of the walk:
Area of the walk = Area of the larger rectangle - Area of the yard = 2596 sq ft - 1836 sq ft = 760 sq ft.
Therefore, the area of the walk is 760 square feet.
To find the area of the walk, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
The outer rectangle measures 36 ft by 51 ft, so the area of the outer rectangle is:
Area of outer rectangle = length × width
Area of outer rectangle = 36 ft × 51 ft
Now, let's calculate the area of the inner rectangle. Since the walk is 4 ft wide, we will reduce 4 ft from each side of the outer rectangle to get the dimensions of the inner rectangle.
The length of the inner rectangle is the outer length minus twice the width of the walk:
Inner length = Outer length - 2 × walk width
Inner length = 36 ft - 2 × 4 ft
The width of the inner rectangle is the outer width minus twice the width of the walk:
Inner width = Outer width - 2 × walk width
Inner width = 51 ft - 2 × 4 ft
Now, we can calculate the area of the inner rectangle using the inner length and width:
Area of inner rectangle = Inner length × Inner width
Area of inner rectangle = (36 ft - 2 × 4 ft) × (51 ft - 2 × 4 ft)
Finally, we can calculate the area of the walk by subtracting the area of the inner rectangle from the area of the outer rectangle:
Area of walk = Area of outer rectangle - Area of inner rectangle
Now let's do the calculations:
Area of outer rectangle = 36 ft × 51 ft
Inner length = 36 ft - 2 × 4 ft
Inner width = 51 ft - 2 × 4 ft
Area of inner rectangle = (36 ft - 2 × 4 ft) × (51 ft - 2 × 4 ft)
Area of walk = Area of outer rectangle - Area of inner rectangle
Area of outer rectangle = 1836 ft²
Inner length = 28 ft
Inner width = 43 ft
Area of inner rectangle = 28 ft × 43 ft
Area of walk = 1836 ft² - (28 ft × 43 ft)
Calculating the values:
Area of outer rectangle = 1836 ft²
Area of inner rectangle = 1204 ft²
Area of walk = 632 ft²
Therefore, the area of the walk is 632 ft².