# 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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