What rule can we use to find the area of a square, given its perimeter?

Question

Perimeter of a square
Input Output Arrow
?
Input Output Arrow
Area of a square

Perimeter of a square (cm) Area of a square (cm
2
)
12 9
20 25
36 81

Divide by 4, then multiply by 2.

Divide by 4, then multiply that number by itself.

Multiply input by itself.

Answer 1

To find the area of a square given its perimeter, you can use the following rule:

1. Divide the perimeter by 4 to find the length of one side of the square.
2. Multiply that number by itself to calculate the area.

This can be summarized in one expression:

• If \( P \) is the perimeter, then the area \( A \) can be calculated as:

  \[ A = \left( \frac{P}{4} \right)^2 \]

Using this method, you can derive the area of a square from its perimeter.

For example:

1. If the perimeter is 12 cm:

   • \( \frac{12}{4} = 3 \) (length of one side)
   • Area \( = 3^2 = 9 \) cm²

2. If the perimeter is 20 cm:

   • \( \frac{20}{4} = 5 \)
   • Area \( = 5^2 = 25 \) cm²

3. If the perimeter is 36 cm:

   • \( \frac{36}{4} = 9 \)
   • Area \( = 9^2 = 81 \) cm²

Therefore, the correct answer is: Divide by 4, then multiply that number by itself.