AREA AND PERIMETER OF QUADRANT

Here we are going to see the how to find area and perimeter of quadrant.

A quadrant is exactly one fourth of any circle.

Area of a quadrant = (1/4)πr²

Perimeter of a quadrant = ((π/2) + 2)r

It has 90 degree angle at the center.

Example 1 :

Find the area of quadrant with radius 7 cm.

Solution :

Here r = 7 cm and π = 22/7.

  =  (1/4) ⋅ (22/7) ⋅ (7)²

  =  (1/4) ⋅ (22/7) ⋅ 7 ⋅ 7

  =  (1/4) ⋅ 22 ⋅ 7

  =  (1/2) ⋅ 11 ⋅ 7

  =  11 ⋅ 3.5  =  38.5 cm²

Example 2 :

Find the area of quadrant with radius 3.5 cm.

Solution :

Here r = 3.5 cm and π = 22/7.

  =  (1/4) ⋅ (22/7) ⋅ (3.5)² 

 =  (1/4) ⋅ (22/7) ⋅ 3.5 ⋅ 3.5

  =  (1/4) ⋅ 22 ⋅ 0.5 ⋅ 3.5

  =  (1/2) ⋅ 11 ⋅ 0.5 ⋅ 3.5

  =  10.5 ⋅ 0.5 ⋅ 3.5 

  =  18.375 cm²

Example 3 :

Find the area of quadrant with radius 64 cm.

Solution :

Here r = 3.5 cm and π = 22/7.

  =  (1/4) x (22/7) x (64)²

  =  (1/4) x (22/7) x 64 x 64

  =  (22/7) x 16 x 64

  =  (22 x 16 x 64)/7  

  =  22528/7 

  =  3218.28 cm²

Example 4 :

Find the perimeter of the quadrant with radius 7 cm.

Solution :

Here r = 7 cm and π = 22/7.

Circumference of quadrant  =  [(Π/2) + 2]r

=  [(22/14) + 2] (7)

  =  [(11/7) + 2] 7

=  ((11 + 14)/7) 7 

=  25 cm 

Example 5 :

Find the perimeter of the quadrant with radius 4.2 cm.

Solution :

Here r = 4.2 cm and π = 22/7.

 =  [(22/14) + 2] (4.2)

  =  [(11/7) + 2] 4.2

=  ((11 + 14)/7) 4.2 

=  (25/7) ⋅ 4.2

=  25(0.6)

=  15 cm

Example 6 : 

Find the perimeter the quadrant with radius 14 cm.

Solution :

Here r = 14 cm and π = 22/7.

 =  [(22/14) + 2] (14)

  =  [(11/7) + 2] 14

=  ((11 + 14)/7) 14 

=  (25/7) ⋅ 14

=  25(2)

=  50 cm

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