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

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

• A. 441 square feet
• B. 324 square feet
• C. 576 square feet
• D. 256 square feet

Answer: (A)

To determine the area of the square garden, we first need to find the length of one side. The perimeter of a square is calculated using the formula: \[ \text{Perimeter} = 4 \times \text{side length} \] Given that the perimeter is 84 feet, we can set up the equation: \[ 84 = 4 \times \text{side length} \] To find the side length, we divide the perimeter by 4: \[ \text{side length} = \frac{84}{4} = 21 \text{ feet} \] Now that we have the length of one side of the square garden, we can calculate the area. The area of a square is calculated using the formula: \[ \text{Area} = \text{side length}^2 \] Substituting the side length we found: \[ \text{Area} = 21^2 = 441 \text{ square feet} \] This calculation confirms that the area of the garden is indeed 441 square feet. This aligns with the choice of A, demonstrating that the answer correctly reflects the area derived from the given perimeter.

To determine the area of the square garden, we first need to find the length of one side. The perimeter of a square is calculated using the formula:

[ \text{Perimeter} = 4 \times \text{side length} ]

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

[ 84 = 4 \times \text{side length} ]

To find the side length, we divide the perimeter by 4:

[ \text{side length} = \frac{84}{4} = 21 \text{ feet} ]

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

[ \text{Area} = \text{side length}^2 ]

Substituting the side length we found:

[ \text{Area} = 21^2 = 441 \text{ square feet} ]

This calculation confirms that the area of the garden is indeed 441 square feet. This aligns with the choice of A, demonstrating that the answer correctly reflects the area derived from the given perimeter.