To find the area of the rectangle, we can multiply the width by the length. The width is given as \( 3x \) and the length is given as \( 2.1x^2 - 4.3x - 6.1 \).
Thus, the area \( A \) can be expressed as:
\[ A = \text{width} \times \text{length} = 3x \times (2.1x^2 - 4.3x - 6.1) \]
Now, to calculate the area:
- Distribute \( 3x \) across the polynomial:
\[ A = 3x \cdot 2.1x^2 + 3x \cdot (-4.3x) + 3x \cdot (-6.1) \]
- Perform the multiplication:
\[ A = 6.3x^3 - 12.9x^2 - 18.3x \]
So, the area of the rectangle is:
\[ \boxed{6.3x^3 - 12.9x^2 - 18.3x} \]