To calculate the area of a square with a side length of 25.4 cm in square inches, follow these steps:
1. Find the area of the square in square centimeters (cm²):
The formula for the area of a square is:
[tex]\[
\text{Area} = \text{side}^2
\][/tex]
Given the side length is 25.4 cm:
[tex]\[
\text{Area in cm²} = 25.4 \, \text{cm} \times 25.4 \, \text{cm} = 645.16 \, \text{cm}^2
\][/tex]
2. Convert the area from square centimeters (cm²) to square inches (in²):
To convert square centimeters to square inches, we use the conversion factor that [tex]\(1 \, \text{cm} = 0.393701 \, \text{in}\)[/tex].
The conversion from cm² to in² requires squaring the conversion factor:
[tex]\[
1 \, \text{cm}^2 = (0.393701 \, \text{in})^2 = 0.15499070401 \, \text{in}^2
\][/tex]
Now, convert the area we found in cm² to in²:
[tex]\[
\text{Area in in²} = \text{Area in cm²} \times 0.15499070401
\][/tex]
Substituting the area in cm²:
[tex]\[
\text{Area in in²} = 645.16 \, \text{cm}^2 \times 0.15499070401 = 100.00010800002916 \, \text{in}^2
\][/tex]
So, the area of the square with a side length of 25.4 cm is approximately [tex]\(645.16 \, \text{cm}^2\)[/tex] or [tex]\(100.00010800002916 \, \text{in}^2\)[/tex].
