The apothem is the line within the polygon that connects the center and a midpoint of any side of the polygon. It is convenient that there is a formula relating area and apothem. Also, a regular octagon is an 8-sided polygon with equal measure of the sides.
A =1/2*apothem*perimeter
Perimeter = 2.5*8 = 20 cm
A=1/2*20*3
A = 30 square cm
Therefore, the area of the regular octagon is 30 square centimeters.