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 quarter circle = (1/4) Π r²

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

It has 90 degree at the center.

Examples

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 circumference 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 circumference of the quad-rant 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 circumference of 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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