. A circle of radius 1 is inscribed inside a polygon with eight sides of equal length, called a regular octagon. That is, each of the eight sides is tangent to the circle, as in the picture on the right.

(a) Calculate the area of the octagon.

(b) If you were to increase the number of sides of the polygon, would the area inside it increase or decrease? What number would the area approach, if any? Explain.

(c) Inscribe a regular octagon inside the same circle. That is, draw a regular octagon such that each of its eight vertexes touches the circle. Calculate the area of this octagon