Answer:
See explanation.
Step-by-step explanation:
The 'base' of a rectangular prism refers to only one side of the rectangular prism, which is a rectangle.
The formula for the area of a rectangle is as follows:

Where A = area, l = length, and w = width.
The 'base' of a cylinder refers to only one side of the cylinder, which is a circle.
The formula for the area of a circle is as follows:

Where A = area and r = radius.
Just in case you typed your question incorrectly and were asking for surface area, here is the formula for surface area for both as well:
Rectangular prism: 
Cylinder: 