standard_description: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
problem_activity: Task
The goal of this task is to explain why the area enclosed by a circle $C$ of radius $r$ is
$\pi r^2$.  Recall that $\pi$ is the ratio of the circumference of a circle to its diameter and that this ratio is independent of the size of the circle.
Draw a picture of a regular octagon $O$ inscribed in $C$.  Find  a formula for the area of the octagon in terms of its perimeter.
Reasoning as in part (a), find a formula for the area of a regular $n$ sided polygon, for $n \geq 3$, inscribed in $C$: the formula should give the area of the polygon  in terms of  its perimeter.
Using your formula from part (b), explain why the area of $C$ is $\pi r^2$.


aligns: no