1. Perimeter and Area of Circles and Sectors I CAN -Find the circumference and area of a circle -Find the arc length of a sector -Find the area of a sector

2. Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft 2. a 45°-45°-90° triangle with leg length 4 in. 3. a 30°-60°-90° triangle with longer leg length 3m

3. A circle is the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol  and its center.  A has radius r = AB and diameter d = CD. Solving for C gives the formula C = d. Also d = 2r, so C = 2r. The irrational number  is defined as the ratio of the circumference C to the diameter d, or

4. Recall from your past years in Math the following formulas:

5. Arc length is related to the circumference of a circle. It is a fraction of the circumference of the circle One way of finding arc length.

6. Finding circumference and arc lengths I. Find the circumference of  P, “circle with center P.” ● P 24 cm C = 2  r C =  d C = 24  cm

7. Finding circumference and arc lengths II. Find the arc length (L) of AB ● 24 cm “piece of the circumference” You can use proportions to easily find the arc length. Part 90 = L Whole 360 24  1 = L 4 24  4L = 24  Cross multiply to solve proportion L = 6  cm Don’t forget units! P ●A ●B Remember the circumference is 24 

8. Finding circumference and arc lengths III. Find the arc length (L) of AB ● 24 cm “piece of the circumference” Don’t forget units! P ●B 80º ●A

9. Just like arc length is related to the circumference of a circle, the area of a sector is related to the area of the circle. The area of a sector is a fraction of the area of the circle

10. One way of finding area of a sector

11. I. Find the area of  P ● P 24 c m A =  r 2 A =  (12) 2 A = 144 cm 2 Don’t forget your units! Finding area of circles and area of sectors

12. II. Find the sector area (S) of sector APB ● 24 cm “piece of the area” You can use proportions to easily find the sector area Part 90 = S Whole 360 144  1 = S 4 144  4S = 144  Cross multiply to solve proportion S = 36  cm 2 Don’t forget units! P ●A ●B Remember the total area is 144 

13. Finding the area of circles and area of sectors III. Find the sector area (S) of sector APB ● 24 cm “piece of the area” S = Don’t forget units! P ●B 80º ●A

14. A segment of a circle is a region bounded by an arc and its chord.

15. Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. ON YOUR OWN FG

16. ON YOUR OWN Find each arc length. Give your answer in terms of  and rounded to the nearest hundredth. GH =  m  4.19 m

17. Find the area of each sector. Give answers in terms of  and rounded to the nearest hundredth. ON YOUR OWN sector HGJ = 52.4 m 2  164.62 m 2