Krishna
0

METHOD 1:

Step 1: Set up a formula for the area of the sector.

            NOTE: Area of the sector = (\frac{l}{2\pi r}) \pi r^2

                        Area of the sector  =   \frac{lr}{2}  (Simplified)

            Where, r = the length of the radius, and l = the length of the arc.


Step 2: Substitute the arc length and radius into the formula.

              Area of the sector  =   \frac{lr}{2}

                Area of the sector  = \frac{3 * 5 \pi }{2}


Step 3: Simplify the values to know the sector area.


METHOD 2:

Step 1: Calculate the central angle by using the arc length formula

              Skill 1: Write the arc length formula

                          Arc length = \theta * radius

                                    \theta = Central angle

              Skill 2: Substitute the known values in the formula.

                             5 \pi = \theta * 3

              Skill 3: Solve for central angle

                                 5 \pi = \theta * 3

                           \frac{5 \pi}{3} = \theta


Step 2: Set up a formula for the sector area

            NOTE: A ratio will need to be constructed. Recall that a circle is composed

            of 360 degrees. Therefore, the following ratio can be made,

                         \frac{\theta}{360} = \frac{\text{sector area} (A_C)}{\text{Total area} (A_T)}

            Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                where, \theta = Central angle.

Step 3: Plug the sector’s central angle measurement into the formula.  

Step 4: Plug the sector’s radius measurement into the formula.  

Step 5: Solve for the area:

            EXAMPLE: Sector area = \frac{\theta}{360} * \pi r^2 (since area = \pi r^2)

                              Sector area = \frac{60}{360}*\left(3.14\right)\left(5\right)^2

                                  Sector area = 13.09 cm^2