## The Formula for the Area of a Circle

## Work Time

# The Formula for the Area of a Circle

Set A contains a 16-gon divided into 16 congruent triangles and the same 16-gon rearranged into a parallelogram made up of the 16 congruent triangles. The perimeter of the polygon is labeled *p* and the apothem is labeled *a*.

Set B contains a circle divided into 16 congruent sections and the same circle rearranged into a parallelogram-like shape, which is made up of the 16 congruent sections. The radius is labeled *r*.

- Look carefully at the two sets of figures. How are they similar?
- What is the length of the parallelogram-like shape formed from the circle? What is the height?
- How could you express the area of the circle in terms of
*r*?

## Hint:

- What is the “apothem” of a circle called?
- What is the perimeter of a circle called?