To solve for the area of the base of the briefcase, we need to use the information given about its volume and height. The briefcase is described as a rectangular prism, and for such a shape, the formula for volume [tex]\( V \)[/tex] is given by:
[tex]\[ V = \text{Base Area} \times \text{Height} \][/tex]
Here, we know:
- The volume [tex]\( V \)[/tex] is [tex]\( 4875 \, \text{cm}^3 \)[/tex]
- The height [tex]\( h \)[/tex] is [tex]\( 10 \, \text{cm} \)[/tex]
We need to find the base area [tex]\( A \)[/tex]. To do so, we rearrange the formula to solve for the base area:
[tex]\[ A = \frac{V}{h} \][/tex]
Substituting the given values into this formula:
[tex]\[ A = \frac{4875 \, \text{cm}^3}{10 \, \text{cm}} \][/tex]
[tex]\[ A = 487.5 \, \text{cm}^2 \][/tex]
Therefore, the area of the base of the briefcase is [tex]\( 487.5 \, \text{cm}^2 \)[/tex].
So, the correct choice is:
[tex]\[ \boxed{487.5 \, \text{cm}^2} \][/tex]
