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.

**Related Topics**

**practice questions with solution****Length of arc****Practice questions on length of arc****Perimeter of square****Perimeter of parallelogram****Perimeter of rectangle****Perimeter of triangle****Area of a circle****Area of Semicircle****Area of Quadrant****Area of sector****Area of triangle****Area of equilateral triangle****Area of scalene triangle****Area of square****Area of rectangle****Area of parallelogram****Area of rhombus****Area of trapezium****Area of quadrilateral****Area around circle****Area of pathways****Area of combined shapes**

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