Step 1; Note down the given values and examine the given figure

Step 2: Find the unknown area by the known areas.

          NOTE: Area of the segment AYB = Area of sector OAYB − Area of ∆OAB

Step 3: Calculate the area of the sector

          [Step 1: Recall the area of the sector formula  

            NOTE: \frac{\theta}{360} * \pi r^2

            Step 2: Substitute all the values in the formula.

          EXAMPLE:   \frac{\theta}{360} * \pi r^2

                        \frac{120}{360}\ *\ 3.14\ *\ 21^2

            Step 3: Simplify the equation

            EXAMPLE:  \frac{1}{3}\cdot\ 3.14\ \cdot\ 441\ cm^2

                                462\ cm^2]

Step 4: Find the area of the triangle

            Skill 1: Recall the area of the circle formula

                      NOTE: \frac{1}{2} base * height

            Skill 2: Construct a line joining the center and the mid point of the chord and

                      note down the changes   

                    NOTE: draw  (O center, M mid point)OM ⊥ AB(Chord) as shown in

                    the figure:- Note OA = OB.  Therefore, by RHS congruence,∆AMO ≅ ∆BMO

                    So, M is the midpoint of AB and ∠ AOM = ∠ BOM = \frac{1}{2}120 = 60 \degree

              Skill 3: Find the height using the trigonometric ratios.

                      EXAMPLE:  Let, OM = x cm

                    So, from ∆OMA ,   \cos 60 = \frac{OM}{OA}

                                     \frac{1}{2} = \frac{x}{21} (since   \cos 60 = \frac{1}{2}

                                    OM = x = \frac{21}{2}

                          Also,

                                    \sin 60 = \frac{AM}{OA}

                                     \frac{\sqrt{3}}{2} = \frac{AM}{21}  (since   \sin 60 = \frac{\sqrt{3}}{2}

                                     AM = \frac{21\sqrt{3}}{2}

  .            Skill 4: Calculate the base of the triangle

                          NOTE: Therefore AB = 2AM 

                          EXAMPLE: AB = 2 * \frac{21\sqrt{3}}{2}

                                             AB = 21 * \sqrt{3}

                Skill 5: Substitute the calculated values in the formula  

                            EXAMPLE: \frac{1}{2} * AB * OM

                                       \frac{1}{2} *(21 * \sqrt{3}) (\frac{21}{2})

                                       \frac{441}{4} \sqrt{3}

Step 5: Determine the area of the segment

        Area of the segment AYB = Area of sector OAYB − Area of ∆OAB

        EXAMPLE: Area of the segment AYB = 462 -   \frac{441}{4} \sqrt{3}

                            Area of the segment AYB = 271.047 cm^2