The problem is asking to find the area of a rectangle with the given dimensions.

We can break the problem into the two dimensions provided:

• Length: $3 \frac{2}{3}$ cm, which can be written as an improper fraction: $3 \frac{2}{3} = \frac{11}{3}$
• Width: $5 \frac{5}{8}$ cm, which can be written as an improper fraction: $5 \frac{5}{8} = \frac{45}{8}$

The area $A$ of a rectangle is calculated by multiplying the length and the width:

$A = \text{Length} \times \text{Width} = \frac{11}{3} \times \frac{45}{8}$

Let's calculate this.The area of the rectangle is $20.625 \, \text{cm}^2$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this problem:

1. How do you convert a mixed number to an improper fraction?
2. How is the area of a rectangle derived from its dimensions?
3. Can you apply the same method to find the area of other geometric shapes?
4. How can you convert the decimal result back into a fraction if needed?
5. What is the significance of using units (e.g., cm$^2$) in area calculations?

Tip: When multiplying fractions, you can simplify by canceling common factors between the numerator and denominator before multiplying.