Certainly! Let's solve the problem step by step.
1. Understand the given side length:
The side length of the square is [tex]\( 10 \frac{2}{5} \)[/tex] cm. This is a mixed fraction, which can be converted to an improper fraction or a decimal for easier calculations.
- Mixed fraction: [tex]\( 10 \frac{2}{5} \)[/tex] means [tex]\( 10 \)[/tex] whole units and [tex]\( \frac{2}{5} \)[/tex] of another unit.
- To convert this to a decimal:
[tex]\( 10 + \frac{2}{5} \)[/tex]
Since [tex]\(\frac{2}{5}\)[/tex] equals [tex]\( 0.4 \)[/tex], the side length is [tex]\( 10.4 \)[/tex] cm.
2. Calculate the area of the square:
The formula for the area of a square is:
[tex]\[
\text{Area} = \text{side length}^2
\][/tex]
With the side length of [tex]\( 10.4 \)[/tex] cm, the area is:
[tex]\[
\text{Area} = 10.4 \times 10.4 = 108.16 \, \text{cm}^2
\][/tex]
3. Calculate the perimeter of the square:
The formula for the perimeter of a square is:
[tex]\[
\text{Perimeter} = 4 \times \text{side length}
\][/tex]
With the side length of [tex]\( 10.4 \)[/tex] cm, the perimeter is:
[tex]\[
\text{Perimeter} = 4 \times 10.4 = 41.6 \, \text{cm}
\][/tex]
So, the side length of the square is [tex]\( 10.4 \)[/tex] cm, the area is [tex]\( 108.16 \, \text{cm}^2 \)[/tex], and the perimeter is [tex]\( 41.6 \)[/tex] cm.
