Perimeter Of The Sector

In this page perimeter of the sector we are going to see formula to find perimeter of sector,example problems.

Formula:

Perimeter of the sector = L + 2r

L - length of sector

r - radius

Now let us see some example problems based on this formula.

Example 1:

Find the perimeter of sector whose area is 324 square cm and the radius is 27 cm.

Solution:

To find perimeter of any sector we need length of arc and radius of sector. In this question we have radius but we don't have length of arc to find L we are using the formula (1/2) L r instead of area of sector.

Area of sector = 324 square units

           (1/2) L x r = 324

                 here r = 27 cm

       (1/2) x L x 27 = 324

                       L = (324 x 2)/27

                       L = 12 x 2

                       L = 24 cm

Now we can find the perimeter.

Perimeter of sector = L + 2r

                          =  24 + 2(27)

                          =  24 + 54

                          =  78 cm  perimeter of the sector


Example 2:

Find the length of arc if the perimeter of sector is 45 cm and radius is 10 cm.

Solution:

Perimeter of sector = 45 cm

Perimeter of sector = L + 2r

                    L + 2r = 45

 here r = 10 cm

                    L + 2 (10) = 45

                    L + 20 = 45

                           L = 45 - 10

                           L = 35 cm


Example 3:

Find the radius of sector whose perimeter and length of arc are 30 cm and 16 cm respectively.

Solution:

 Perimeter of sector = 30 cm

 length of arc = 16 cm

Perimeter of sector = L + 2r

                        L + 2r = 30

                           16 + 2r = 30

                                  2r = 30 - 16

                                  2r = 14

                                   r = 14/2

                                   r = 7 cm.


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