Question

The area of a regular octagon is 25 cm2. What is the area of a regular octagon with sides four times as large?

Answer 1

Regular polygon area = n*side^2 / (4 * tan (180/n))
where "n" is number of sides
The formula is dependent on the side^2 term,
So, if we have an octagon that has sides 4 times as large, that means the area will be sixteen times larger.
side^2 = 4^2 = 16
So we multiply 25 cm^2 by 16 and we get
400 square centimeters.

Source:
http://www.1728.org/polygon.htm