# Lesson 2 From Polygons to Circles Solidify Understanding

Calculate the perimeter and area for each figure.

### 1.

perimeter:

area:

### 2.

perimeter of green (both inside and outside):

area of green:

### 3.

perimeter:

area:

### 4.

perimeter:

area:

### 5.

perimeter:

area:

### 6.

perimeter:

area:

### 7.

A circle and several congruent squares with side lengths equal to the radius of the circle are shown. Use these squares to estimate how many squares it takes to fill in the area of the circle. State what you notice. (Try using tracing paper or create cutouts to make a good estimate.)

### 8.

Which polygon has an area and perimeter closest to the circle in which it is inscribed? Why?

### 9.

Given that the radius of each circle in the previous problem is

Shape | One Interior Angle | Length of One Side | Area of Figure |
---|---|---|---|

Triangle | |||

Square | |||

Pentagon | |||

Hexagon | |||

Octagon | |||

Decagon | |||

Circle |

### 10.

Explain how a circle can be cut into sectors and reconfigured to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

### 11.

Explain how a circle can be broken into several rings or interior circles that can be rearranged to appear approximately as a polygon that could have its area calculated using a standard formula. (Use a diagram with your explanation.)

Use the given circle in the following problems to find the indicated measures:

circumference of the entire circle

the fractional part of the circle represented by the ratio of the central angle to

the shortest arc length

that is intercepted by the central angle

(The shortest arc length from

### 12.

circumference of circle:

ratio of central angle to

: the shortest arc length

:

### 13.

circumference of circle:

ratio of central angle to

: the shortest arc length

:

### 14.

circumference of circle:

ratio of central angle to

: the shortest arc length

:

### 15.

circumference of circle:

ratio of central angle to

: the shortest arc length

: