Geometry 10-7 Area and Circumference of a Circle by ewghwehws

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```									Presented by MJ Lund
   If a circle has a circumference of C units and a
radius of r units, then C = 2πr.
   If a circle has an area of A square units and a
radius of r units, then A = πr2

r
Example #1:
Find the area of the shaded region
18 yd
Solution:

Plan: Area of square - Area of the circle

Formulas: A = s2 –      πr2

A = 502 - π182

A = 2500 - 324π sq yds
50 yd
or A = 1482.12 sq yds.
y

x
Example #2:
(2,-5)
9
Find the area of a circle
with the equation
(x-2)2 + (y+5)2 = 81

•This is a circle whose center point is (2,-5) and
•Therefore, A = π r2 and A = (π)(9)2 and so the
A = 81π or about 254.5 sq units
Area of a Sector
What is a “sector”?

A sector is a section of the circle bound by two radii and their
intercepted arc.

In simpler terms, the shape of a slice of pizza.

sector
Calculating the area of a sector

Once again, you are confronted with
another formula. Here is the area
of a sector formula:
mAB
Area    r   2

360
The formula calculates the total area of the circle first, then the
formula takes the arc measure and divides by 360 to calculate
the portion of the total area called a sector.
Area of a sector example #3:
Given the following information with the
diagram, calculate the area of the sector.

mAB
Area    r 2 
360
120
Area    5 
2         Plug in numbers for variables
360
1
A
5 cm                Area    25             Simplified values
3
120
25
Area                      Multiplied
3
78.54           2
Area           26.18cm       Final answer
3
B
Calculating the area of a
segment
What’s a segment?
A segment of a circle is a region bounded by a chord and its
intercepted arc.
Segment calculation process

1. Calculate the area of the sector.
2. Calculate the area of the triangle in
the sector.
3. Subtract the area of the triangle
from the area of the sector.
Segment example #4:
Given the following information with the diagram,
calculate the area of the segment of the circle.

mAB
sector    r 
2
Area of sector formula
A                                360

90
sector   12 
2         Plug in values for variables
360
1
sector   144              Simplified
B                         4
O
144
12 yd

sector                        Multiplied
4
sector  36 113.1yd 2           Sector answer

continue
Segment example #4 continued:
Now that you have calculated the sector, calculate
the area of the triangle inside the sector.

1
A            triangle        b  h          Area of a triangle formula
2
1        The base and height are 12 because each
triangle  12 12       represent radii of the circle.
2
1           Multiplied
triangle      144
B                 2
O
triangle  72yd 2
12 yd                                 Multiplied

continue
Segment example #4 concluded:
The last stage is to subtract the area of the
triangle from the area of the sector.

segment  sector  triangle
A

segment  113.1yd 2  72yd 2       Plug in values

segment  41.1yd 2         Final answer

B
O     12 yd

Segment area = 41.10 square yds

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