Question

how can you cut apart and rearrange a circle to find the formula for i area? 1 of 4 question cut the circle into slices and arrange them into triangles. cut the circle into slices and arrange them into a parallelogram. cut the circle in half and use the two straight edges to forr two sides of a square. straighten out the outside edge of the circle and measure its length.

Explanation:

When deriving the area formula of a circle ($A = \pi r^{2}$), a common geometric method is to cut the circle into many small sectors (slices). Then, these sectors can be rearranged. As the number of sectors increases, the shape formed by these sectors approaches a parallelogram. The base of this parallelogram is approximately half of the circumference of the circle ($\frac{1}{2}\times2\pi r=\pi r$) and the height is approximately the radius ($r$) of the circle. Using the area formula of a parallelogram ($A = base\times height$), we get $A=\pi r\times r=\pi r^{2}$. Cutting into triangles or using a square - related method (cutting in half for a square) is not the standard way for this derivation. Straightening the outside edge (circumference) alone does not directly lead to the area formula derivation in the context of geometric rearrangement for area formula proof.

Answer:

Cut the circle into slices and arrange them into a parallelogram.