standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Problem 1
a.   Create as many rectangles as you can with a perimeter of 16 units. Find the area of each rectangle that you found. Then record the length, width, perimeter, and area of each rectangle in the table below:
| **                Length (units)               ** | **                Width (units)               ** | **                Perimeter (units)               ** | **                Area (square units)               ** |
|---------------------------------------------------|--------------------------------------------------|------------------------------------------------------|--------------------------------------------------------|
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
|                                                   |                                                  |                                                      |                                                        |
b.   What do you notice about the rectangles you created? What do you wonder?
Problem 2
What is the greatest area you can make with a rectangle that has a perimeter of 20 units?


aligns: no