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Questions Answered in "Area of a Segment of a Circle"

What is the segment of a circle?

How is the segment of a circle different than the sector of a circle?

How do you find the area of a segment of a circle?

Area of a sector formula example

Area Formula of a Segment = Area of Sector - Area of Triangle

Find the area of the following segment

Area formula of a semi-circle = 1/2πr^2

Area formula of a quarter circle circle = 1/2πr^2

Use this formula when the central angle is in radians

area of sector graphic
video tutorial finding area of a sector

Area of a Sector Formula

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area sector/circle

​Transcript Sector Area
Hi welcome to MooMooMath. Today we are going to look at sector area. The best way to explain sector area is to think of it as a pizza slice. So if I have a circle and take out a slice of it, that what I call sector area. OK we need to know a couple of pieces of information to plug into our area formula. We need to know the radius and the measure of the arc. The measure of the arc is equivalent to the central angle. Since this is a 90 degree angle this means the arc angle is also 90 degrees. Now let’s put it into our formula. Let me explain the formula. The measure over 360. Notice if I put 90 over 360, I will reduce that to one fourth of the circle. As you can see 90 degrees is one fourth of the circle. Then I will multiple this by the area which is pi R squared. If I know the whole area of the circle and divide into fourths I will know the area of just this slice. So the area of the circle is pi times my radius, my radius is 8 so 8 squared is 64 so I will take one fourth times pi times 64 and one fourth of 64 is 16 pi You can leave your answer like that or you can multiple it out. So 16 times 3.14 which is 50.4 and it is always the units squared. Let me pop up the rules for area sector. The area of a sector is like a pizza slice you find the area of a circle times the fraction of the circle that you are finding. Hope this video helpful.

steps for finding the area of a sector with a central angle of 90 degrees
Take the measure of the central angle and divide by360
r =8 
Finding the area of a sector explained
Common Core Standard: HSG.C.B.5    High School Math
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π= pi, which equals 3.14
r= radius of circle ( Distance from the center of the circle to the outside edge)​

​½ × θ  × r^2

measure of central angle/360 * pir^2
circle with measure of central angle
Use this area of sector formula when the central angle is in degrees
= 50.24 degrees
What is the area of a sector with a central angle of 90 degrees and a radius of 8 units?
circle with green section
yellow and white circle
 You can convert from degrees to radians and radians to degrees before using the area calculator.
Result: - the ultimate unit conversion resource.

Area of a Segment Formula

segment of a circle /sector of a circle
Segment: the segment would be the area formed when you cut the sector with a chord. ( see highlighted area)
Sector: the sector would be the entire slice including the segment
area of a segment
The video explains how to use the following formula to find the area of the segment
n/360 times pirsquared -1/2base x height
Area of Sector Formula
Area of Triangle Formula
arrow point to area triangle formula
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Area of a Sector Formula