Question

If the perimeter of a square is 12 cm, what is the area?
Is there any other possible output that would be true when the perimeter of the square is 12 cm? In other words, if the perimeter of a square is 12 cm, can the area be anything other than 9 cm
2
?
Square

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

Yes

No

Answer 1

To find the area of a square given its perimeter, we start with the formula for the perimeter \(P\) of a square, which is given by:

\[
P = 4s
\]

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

If the perimeter is 12 cm, we can solve for \(s\):

\[
4s = 12 \implies s = \frac{12}{4} = 3 \text{ cm}
\]

Now, we can calculate the area \(A\) of the square using the formula:

\[
A = s^2
\]

Substituting in the value we found for \(s\):

\[
A = 3^2 = 9 \text{ cm}^2
\]

Thus, if the perimeter of a square is 12 cm, the area is always \(9 \text{ cm}^2\).

Now, addressing your second question: Can the area be anything other than \(9 \text{ cm}^2\) given that the perimeter is \(12 \text{ cm}\)?

The answer is **No**. The only possible area when the perimeter is \(12 \text{ cm}\) is indeed \(9 \text{ cm}^2\).

So the correct answer is:
**No**.