To find the area of a rectangle with the given dimensions, we can follow these steps:
1. Convert the mixed numbers to improper fractions:
- The length of the rectangle is given as [tex]\(3 \frac{5}{6} \text{ cm}\)[/tex].
- First, convert [tex]\(3 \frac{5}{6}\)[/tex] to an improper fraction:
[tex]\[
3 \frac{5}{6} = 3 + \frac{5}{6} = \frac{18}{6} + \frac{5}{6} = \frac{23}{6}
\][/tex]
- The width of the rectangle is given as [tex]\(1 \frac{3}{5} \text{ cm}\)[/tex].
- Next, convert [tex]\(1 \frac{3}{5}\)[/tex] to an improper fraction:
[tex]\[
1 \frac{3}{5} = 1 + \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5}
\][/tex]
2. Convert the improper fractions to decimals for easier multiplication:
- The length in decimal form:
[tex]\[
\frac{23}{6} \approx 3.8333
\][/tex]
- The width in decimal form:
[tex]\[
\frac{8}{5} = 1.6
\][/tex]
3. Multiply the length and width to find the area:
- Use the approximate decimal values:
[tex]\[
\text{Area} = 3.8333 \times 1.6 \approx 6.1333 \text{ square centimeters}
\][/tex]
Therefore, the dimensions of the rectangle and the calculated area are:
- Length: approximately [tex]\(3.8333 \text{ cm}\)[/tex]
- Width: exactly [tex]\(1.6 \text{ cm}\)[/tex]
- Area: approximately [tex]\(6.1333 \text{ square centimeters}\)[/tex]
So, the area of the rectangle is [tex]\( \boxed{6.1333} \text{ square centimeters}\)[/tex].
