1. Bell Ringer
1. What is the proportion to determine arc length?
2. What is the difference between arc length and arc measure?
3. How do you find the area of a circle?

2. Area of a Sector
Tuesday, November 20, 2018

3. What is a sector?
A sector is a portion of a circle… like a slice of pizza is a portion of the whole pie.

4. How do we find the Area of a Sector?
Since a sector is a portion of a circle, its area is a portion of the entire area of the circle. As stated yesterday, circles are proportional.
Yesterday we learned: 𝑨𝒓𝒄 𝑴𝒆𝒂𝒔𝒖𝒓𝒆 360° = 𝑨𝑟𝑐 𝑳𝑒𝑛𝑔𝑡ℎ 𝑪𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
Today we extend that to the area of a circle:
𝐴𝑟𝑐 𝑀𝑒𝑎𝑠𝑢𝑟𝑒 360° = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑆𝑒𝑐𝑡𝑜𝑟 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝐶𝑖𝑟𝑐𝑙𝑒 AND/OR
𝐴𝑟𝑐 𝐿𝑒𝑛𝑔𝑡ℎ 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑨𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑺𝑒𝑐𝑡𝑜𝑟 𝑨𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑪𝑖𝑟𝑐𝑙𝑒

5. Remember your formulas…
Circumference:
C = 2𝜋𝑟
C = 𝜋𝑑
Area:
𝐴=𝜋 𝑟 2

6. Examples Find the area of a sector: 1. Radius 4 ft, arc measure 80º
2. Radius 9 in, central angle 60º
3. Central angle 98º, arc length 8.2 cm
4. Central angle 138º, arc length 24.6 ft
Find the radius of a circle:
5. Sector area 59 in2, central angle 40º
6. Sector area 8 in2, central angle 72º

7. Classwork
Geometry book
p #3-33 odd
Homework
Area of a Sector

8. Remember… in circles things are proportional.
Exit Ticket
1. How do you find the area of a sector given radius and arc measure?
2. How do you find the area of a sector given central angle and arc length?
3. How do you find the radius of a circle given area of the sector and central angle?