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

**Related Topics**

**Perimeter of sector****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 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**