DERIVING THE FORMULA FOR THE AREA OF A SECTOR Adapted from
Walch Education
Slide 3
Key Concepts 3.4.2: Deriving the Formula for the Area of a
Sector 2 A sector is the portion of a circle bounded by two radii
and their intercepted arc.
Slide 4
Key Concepts, continued 3.4.2: Deriving the Formula for the
Area of a Sector 3 To find the area of a sector,, when the central
angle is given in radians, we can set up a proportion using the
area of a circle, We can solve this proportion for the area of the
sector and simplify to get a formula for the area of a sector in
terms of the radius of the circle and the radian measure of the
central angle .
Slide 5
Key Concepts, continued 3.4.2: Deriving the Formula for the
Area of a Sector 4 To find the area of a sector when the central
angle is given in degrees, we can set up a proportion using the
area of a circle.
Slide 6
Practice 3.4.2: Deriving the Formula for the Area of a Sector 5
A circle has a radius of 24 units. Find the area of a sector with a
central angle of 30.
Slide 7
Solution 3.4.2: Deriving the Formula for the Area of a Sector 6
1. Find the area of the circle. 2. Set up a proportion.
Slide 8
Solution, continued 3.4.2: Deriving the Formula for the Area of
a Sector 7 3. Multiply both sides by the area of the circle to find
the area of the sector. The area of the sector is approximately
150.80 units 2.
Slide 9
Your Turn. 3.4.2: Deriving the Formula for the Area of a Sector
8 A circle has a radius of 6 units. Find the area of a sector with
an arc length of 9 units.