standard_description: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
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