To find the area of rectangle A, we can use the information provided about the dimensions of the rectangles.
Suppose the dimensions of rectangle B are \( l \) (length) and \( w \) (width). The area of rectangle B is given by:
\[ \text{Area of rectangle B} = l \times w = 128 \text{ sq cm} \]
Since rectangle A has dimensions that are four times those of rectangle B, the dimensions of rectangle A will be:
\[ \text{Length of rectangle A} = 4l \] \[ \text{Width of rectangle A} = 4w \]
The area of rectangle A can be calculated as follows:
\[ \text{Area of rectangle A} = \text{Length of rectangle A} \times \text{Width of rectangle A} = (4l) \times (4w) = 16lw \]
Now we can substitute the area of rectangle B into this equation:
\[ 16lw = 16 \times (l \times w) = 16 \times 128 = 2048 \text{ sq cm} \]
Thus, the area of rectangle A is:
\[ \text{Area of rectangle A} = 2048 \text{ sq cm} \]
The correct answer is:
D. 2,048 sq cm