Quadrant





In this page quadrant we are going to see the how to find area and perimeter of any this shape.

A quad-rant is exactly one fourth of any circle.

In the above circle shaded portion is known as quad-rant.

Area of quad-rant = (1/4) Π r²

A quad-rant has 90 degree at the center.

Example 1:

Find the area of quad-rant with radius 7 cm

Solution:

Here r = 7 cm and Π = 22/7

                            = (1/4) x (22/7) x (7)²                 

                            = (1/4) x (22/7) x 7 x 7

                            = (1/4) x 22 x 7

                            = (1/2) x 11 x 7

                            = 11 x 3.5 

                            = 38.5 cm²



Example 2:

Find the area of quad-rant with radius 3.5 cm

Area of quad-rant = (1/4) Π r²

Solution:

Here r = 3.5 cm and Π = 22/7

                            = (1/4) x (22/7) x (3.5)²                 

                            = (1/4) x (22/7) x 3.5 x 3.5

                            = (1/4) x 22 x 0.5 x 3.5

                            = (1/2) x 11 x 0.5 x 3.5

                            = 10.5 x 0.5 x 3.5 

                            = 18.375 cm²


Example 3:

Find the area of quad-rant with radius 64 cm

Area of quad-rant = (1/4) Π r²

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


Perimeter of a quad-rant = Πr/2

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

Example 1:

Find the circumference of the quad-rant with radius 7 cm.

Solution:

Perimeter of a quad-rant = Πr/2

                           Here r = 7 cm and  Π = 22/7

                                        = [(22/7) x 7]/2

                                        = 22/2

                                        = 11 cm


Example 2:

Find the circumference of the quad-rant with radius 4.2 cm.

Solution:

Perimeter of a quadrant = Πr/2

                           Here r = 4.2 cm and  Π = 22/7

                                        = [(22/7) x 4.2]/2

                                        = (22 x 0.6)/2

                                        = (11 x 0.6)

                                        = 6.6 cm


Example 3:

Find the circumference of the quad-rant with radius 14 cm.

Solution:

Perimeter of a quad-rant = Πr/2

                           Here r = 14 cm and  Π = 22/7

                                        = [(22/7) x 14]/2

                                        = (22 x 2)/2

                                        = (44/2)

                                        = 22 cm


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