Figure Segment of a Circle

In geometry, a circular segment also circle segment. It is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center.It is shown in figure bellow.
  

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Example of figure segment of a circle:

Example 1
Radius of the circle is 15 cm, angle of the Segment of a circle is 45 degree. Find the area of the Segment of a circle is shown in figure.


Solution:
Area of the circle = `1/2` r²`theta` - sin `theta`

                            = `1/2` r²( `pi/180` *`theta` - sin `theta`)                       

                             =0.5*15²(`pi/180` *45-(sin 45))

                             =112.5(0.785-0.7071)

   Area of the Segment of a circle=8.77 cm²

Example 2
          Radius of the circle is 10 cm, angle of the Segment of a circle is 55 degree. Find the area of the Segment of a circle is shown in figure.
 
Solution:

Area of the circle = `1/2` r²`theta` - sin `theta`

                            = `1/2` r²( `pi/180` *`theta` - sin `theta`)                       

                             =0.5*10²(`pi/180` *50-(sin 50))

                             =50(0.873-0.766)

   Area of the Segment of a circle=5.53 cm²

Example 3
Radius of the circle is 15 cm, angle of the Segment of a circle is 85 degree. Find the area of the Segment of a circle is shown in figure.

Solution:
Area of the circle = `1/2` r²`theta` - sin `theta`

                            = `1/2` r²( `pi/180` *`theta` - sin `theta`)                       

                             =0.5*15²(`pi/180` *85-(sin 85))

                             =112.5(1.484-0.996)

   Area of the Segment of a circle=54.9 cm²

Example 4
Radius of the circle is 15 cm, angle of the Segment of a circle is 105 degree. Find the area of the Segment of a circle is shown in figure.
Solution:
Area of the circle = `1/2` r²`theta` - sin `theta`

                            = `1/2` r²( `pi/180` *`theta` - sin `theta`)                       

                             =0.5*15²(`pi/180` *105-(sin 105))

                             =112.5(1.833-0.9659)

   Area of the Segment of a circle= 97.54 cm²

Example 5
Radius of the circle is 15 cm, angle of the Segment of a circle is 110 degree. Find the area of the Segment of a circle is shown in figure.

Solution:
Area of the circle = `1/2` r²`theta` - sin `theta`

                            = `1/2` r²( `pi/180` *`theta` - sin `theta`)                       

                             =0.5*15²(`pi/180` *110-(sin 110))

                             =112.5(1.92-0.9396)

Area of the Segment of a circle=110.29 cm²