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
Find the area of the shaded region
Plan: Area of square - Area of the circle
Formulas: A = s2 – πr2
A = 502 - π182
A = 2500 - 324π sq yds
or A = 1482.12 sq yds.
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
whose radius is 9.
•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
In simpler terms, the shape of a slice of pizza.
Calculating the area of a sector
Once again, you are confronted with
another formula. Here is the area
of a sector formula:
Area r 2
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.
Area r 2
2 Plug in numbers for variables
5 cm Area 25 Simplified values
Area 26.18cm Final answer
Calculating the area of a
What’s a segment?
A segment of a circle is a region bounded by a chord and its
Segment calculation process
1. Calculate the area of the sector.
2. Calculate the area of the triangle in
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.
Area of sector formula
2 Plug in values for variables
sector 144 Simplified
sector 36 113.1yd 2 Sector answer
Segment example #4 continued:
Now that you have calculated the sector, calculate
the area of the triangle inside the sector.
A triangle b h Area of a triangle formula
1 The base and height are 12 because each
triangle 12 12 represent radii of the circle.
triangle 72yd 2
12 yd Multiplied
Segment example #4 concluded:
The last stage is to subtract the area of the
triangle from the area of the sector.
segment sector triangle
segment 113.1yd 2 72yd 2 Plug in values
segment 41.1yd 2 Final answer
O 12 yd
Segment area = 41.10 square yds