How can we use the regular polygon area formula "A=1/2(apothem)(perimeter)" to find the formula for the area of a circle?

1. What happens to the appearance of the regular polygon as the number of sides increases?[br][br]2. What happens to the length of the apothem as the number of sides increases? [br]What length does it approach?[br][br]3. What type of relationship exists between the number of sides and the length of each side?[br][br]4. What does the perimeter of the polygon appear to approach as the number of sides becomes larger?[br][br]5. Write the equation for the area of the polygon if the number of sides is infinite: