Geometry

Area of a Sector

Sector Area Formula

There are two sector area formulas; one for a sector measured in radians, and another for a sector measured in degrees. They are given as:
Radians: A = 12θr2
Degrees: A = 1360θπr2
Where A is the area, θ is the sector angle, and r is the radius.

area of a sector

Example Problems

Problem 1:
Find the area of a sector with an angle of 90 degrees and a radius of 10.
Solution:
1.) Plugging the given dimensions into the formula, we get:
A = 1360θπr2
A = 1360(90)π(102) = 25π
2.) The area is 25π.

Problem 2:
The sector from problem 1 is changed so that the diameter is 10 instead of the radius being 10. What is the new area?
Solution:
1.) First, let’s convert diameter to radius.
2r = d
2r = 10
r = 5
2.) Now let’s plug the radius and angle into the formula.
A = 1360θπr2
A = 1360(90)π(52) = 6.25π
3.) The area is now 6.25π.

Result :

Worksheet 1

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Cheat sheet

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Area Of A Sector

how to find the area of a sector

To find the area of a sector, take the angle measurement and divide it by 360. Use this to multiply the area of the circle.

AREA OF A SECTOR FORMULA

Area=πr^2 (Angle/360) 

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EXAMPLE PROBLEM 1

Find the area of a sector with an angle of 90 and a radius of 10 Plug everything into the formula Area=π10^2 (90/360) The area is 25 π

EXAMPLE PROBLEM 2

Find the area of a sector with an angle of 90 and a diameter of 10 First, we need to find the radius. To do this, we take 10/2. The radius is 5. Now plug everything into the formula. The Area is 6.25 π
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