Answer to Question #111184 in Geometry for nyleve

Question

Alice cuts a circular piece of paper into sectors of equal sizes. She rearranges all sectors in a plane without gaps or overlaps with alternating curved parts. Which of these relates the area of the new arrangement to the area of the original whole piece of paper?

Answer 1

The sectors form a parallelogram with a height of $r$ and base of $\pi r$ . So the area of original circular piece of paper was $\pi r\times r = \pi r^2$