Krishna
0

Step 1: Use the relationship between circumference and radius to find the radius of the circle.  

         NOTE: Circumference C = 2 \pi r

             r = \frac{C}{2*\pi}

            Find the radius of the circle

            EXAMPLE: r = \frac{C}{2*\pi}​ r = \frac{22}{2*\pi} (since \pi = \frac{22}{7} = 3.14)

             r = \frac{7}{2}

Step 2: Calculate the area of the circle.

            Total area of the circle = \pi r^2


Step 3: 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)}

               where, \theta = Central angle


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


Step 4: Plug the given or calculated area measurement into the formula.

EXAMPLE: \frac{26}{360} = \frac{\text{sector area} (A_C)}{\text{46} (A_T)}


Step 5: Solve the area.


EXAMPLE: \frac{\theta}{360}=\frac{Sector\ area\ \left(A_C\right)}{Total\ area\ \left(A_T\right)}

                   \frac{26}{360} = \frac{\text{sector area} (A_C)}{\text{46} (A_T)}

                   \frac{26}{360} * 46 = \text{Sector area} (A_C)

                    sector area = 3.32