The base of a cone is its single circular face, the widest circle in the stack of circles that runs up or down the cone's length. For instance, if you filled up an ice cream cone, the base would be its top. The cone's base is a circle, so if you know a cone's radius, you can find the area of the base by using the area formula for a circle.
Radius and Pi

The radius, usually noted as "r," of a cone is the distance from the center of the cone's base to the side of the cone's base. Pi is defined as the circumference of a circle divided by its diameter. It always has the same value: roughly 3.14. Depending on the level of precision you need in your calculations, pi can be extended to an endless number of digits after the decimal point. For example, pi extended to seven digits would be 3.1415926. However, 3.14 is considered a good enough approximation for basic geometry equations.
Finding the Base's Area

A circle's area, or A, and that of the base of the cone, is equal to pi times its radius squared: A = pi x r^2. A number squared is equal to that number multiplied by itself. If your cone had a radius of 7 inches, you would compute the area as follows:
A = pi x 7 inches ^2 = 3.14 x 7 inches x 7 inches = 153.86 square inches
References
 Photo Credit George Doyle/Stockbyte/Getty Images