Area of a Circle  Wedge/Sector Demonstration
We know that the area of a circle is: A=πr². But this is actually hard to prove.[br][br]So we cut the circle into wedges and place half of the wedges faceup and half facedown. [br]The hangingout yellow pieces always "fillup" the empty areas of the rectangle with A=πr²[br][br]As the number of wedges increases, the teal line > radius and the hangingout pieces start to fit inside the rectangle.[br]Isn't that cool? Showing this mathematically is called calculus!
What is the total length of the curved parts of the yellow wedges?[br]Why did we label the xaxis with units of π and the yaxis with units of numbers?
'...in a square'
A blue square is inscribed in a green square. Answer the questions below! 

What fraction of the area of the green square is occupied by the blue square? What fraction of the perimeter of the the green square is the perimeter of the blue square? A blue rectangle is inscribed in a green square. What fraction of the area of the green square is occupied by the blue rectangle? What fraction of the perimeter of the the green square is the perimeter of the blue rectangle? 