Optimal Quadrilaterals

What is the largest possible area that can be found in a quadrilateral with perimeter 12? We will call this shape an optimal quadrilateral for this exploration.
What are some properties of the optimal quadrilateral? What is another name for this quadrilateral?

Try this exploration again, but use a different perimeter. Is the optimal quadrilateral the same or different? Do you think the results of the exploration will be the same, regardless of the perimeter used? Explain why or why not.