The area of a regular octagon of side length a is A.
(a) Find the time rate of change of area of the octagon if its side length is being increased at a constant rate of `beta m//s`. Is the time rate of change of area of the octagon constant with time ?
(b) Find the approximate change in area of the octagon as the side length is increased from 2.0 m to 2.001 m.

Answer

(a) `4(sqrt(2)+1)a beta`. No, it is not a constant
(b) `0.0019 m^(2)`