Let's begin by solving the problem step-by-step:
Given:
- A square sheet of paper with side length of [tex]\(25 \text{ cm}\)[/tex].
- A small square portion with side length of [tex]\(9 \text{ cm}\)[/tex] is cut out from it.
To Find:
- The area of the remaining portion of the paper after the small square has been cut out.
1. Calculate the Area of the Original Square Sheet:
The area [tex]\(A\)[/tex] of a square is given by the formula:
[tex]\[
A = \text{side length}^2
\][/tex]
For the original square sheet,
[tex]\[
A_{\text{original}} = 25 \text{ cm} \times 25 \text{ cm} = 625 \text{ cm}^2
\][/tex]
2. Calculate the Area of the Small Square that is Cut Out:
Similarly, for the small square,
[tex]\[
A_{\text{cut-out}} = 9 \text{ cm} \times 9 \text{ cm} = 81 \text{ cm}^2
\][/tex]
3. Calculate the Area of the Remaining Portion of the Paper:
The area of the remaining portion is the area of the original square sheet minus the area of the small square cut out:
[tex]\[
A_{\text{remaining}} = A_{\text{original}} - A_{\text{cut-out}}
\][/tex]
Substitute the respective areas calculated:
[tex]\[
A_{\text{remaining}} = 625 \text{ cm}^2 - 81 \text{ cm}^2 = 544 \text{ cm}^2
\][/tex]
Therefore, the area of the remaining portion of the paper is [tex]\(544 \text{ cm}^2\)[/tex].
