If the perimeter of a square garden is 84 feet, what is the area of the garden?

To find the area of a square garden given its perimeter, first, we need to determine the length of one side of the square. The formula for the perimeter of a square is calculated as four times the length of one side.

Given that the perimeter is 84 feet, we can set up the equation:

Perimeter = 4 × side length

84 = 4 × side length

To find the side length, divide both sides of the equation by 4:

side length = 84 ÷ 4 = 21 feet.

Now that we have the length of one side, we can calculate the area of the square. The area of a square is given by the formula:

Area = side length × side length.

Thus:

Area = 21 feet × 21 feet = 441 square feet.

This calculation confirms that the area of the garden is indeed 441 square feet. The area is correctly identified, which corresponds with the provided option of B. This understanding of the relationship between perimeter, side length, and area is essential when solving similar problems involving squares or other geometric shapes.