What is the area of a square with a perimeter of 20 cm?

Question

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

Answer 1

To find the area of a square when the perimeter is given, you can use the following steps:

1. The formula for the perimeter \( P \) of a square is given by:

   \[ P = 4s \]

   where \( s \) is the length of one side of the square.

2. Given that the perimeter is 20 cm, we can solve for the side length \( s \):

   \[ 20 = 4s \]

   Dividing both sides by 4:

   \[ s = \frac{20}{4} = 5 \text{ cm} \]

3. Now, to find the area \( A \) of the square, we use the formula:

   \[ A = s^2 \]

   Substituting \( s = 5 \) cm:

   \[ A = 5^2 = 25 \text{ cm}^2 \]

So, the area of the square with a perimeter of 20 cm is 25 cm².