If the perimeter of a square is 40cm, what is the area of the square 

To find the area of a square given its perimeter, follow these steps:

1. The perimeter \( P \) of a square is the sum of all its four sides, and since all sides of a square are equal, we can express the perimeter as:
   \[
   P = 4 \times s
   \]
   where \( s \) is the length of one side of the square.

2. In this case, the perimeter is 40 cm, so:
   \[
   40 = 4 \times s
   \]

3. Solving for \( s \):
   \[
   s = \frac{40}{4} = 10 \, \text{cm}
   \]

4. The area \( A \) of a square is given by:
   \[
   A = s^2
   \]

5. Substituting \( s = 10 \, \text{cm} \) into the area formula:
   \[
   A = 10^2 = 100 \, \text{cm}^2
   \]

Thus, the area of the square is **100 cm²**.

Would you like further explanation or have any other questions?

Here are some related questions you might find helpful:
1. If the area of a square is 81 cm², what is its perimeter?
2. What is the relationship between the diagonal of a square and its area?
3. How do you find the side length of a square if only the diagonal is given?
4. How does the formula for the area of a square differ from the formula for the area of a rectangle?
5. Can you find the area of a square when given its diagonal length?

**Tip:** Remember, the perimeter of any polygon is the total length around it, while the area is the measure of the surface enclosed by the shape.

If the perimeter of a square is 40cm, what is the area of the square?

Learn how to calculate the area of a square when its perimeter is 40 cm. This step-by-step guide explains the key geometric formulas, including how to find the side length from the perimeter and calculate the area of the square. Ideal for students in Grades 5-7.

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