A square playground has a perimeter of 2800 feet. It has a paved 6-foot walkway around it. What is the area of the walkway in square feet?
you know how to find the area of a square, right?
So, consider that the sides of the entire area are 12 feet longer than those of the playground.
Subtract the area of the playground from the entire area.
To find the area of the walkway, we need to determine the dimensions of the square playground including the walkway.
Let's denote x as the length of one side of the square playground.
Since the playground has a paved 6-foot walkway around it, the length of one side of the entire square (including the walkway) would be (x + 12) feet.
The perimeter of a square is found by multiplying the length of one side by 4. Therefore, we can write the equation:
Perimeter of the playground + Perimeter of the walkway = 2800 feet
(4x) + (4(x + 12)) = 2800
Simplifying the equation:
4x + 4x + 48 = 2800
8x + 48 = 2800
8x = 2752
x = 344
Now we have the length of one side of the square playground, which is 344 feet.
To find the area of the walkway, we subtract the area of the square playground from the area of the square that includes the walkway.
The area of the square playground is found by squaring the length of one side:
Area of playground = x^2 = 344^2 = 118,336 square feet
The area of the square that includes the walkway is found by squaring the length of one side including the walkway:
Area of square with walkway = (x + 12)^2 = (344 + 12)^2 = 356^2 = 126,736 square feet
Finally, we can find the area of the walkway by subtracting the area of the playground from the area including the walkway:
Area of walkway = Area of square with walkway - Area of playground
Area of walkway = 126,736 square feet - 118,336 square feet
Area of walkway = 8,400 square feet
Therefore, the area of the walkway is 8,400 square feet.