Area Of Quadrant

What is Quadrant?

A circle is defined as the locus of all the points that are equidistant from the center. Now, a quadrant is one-fourth section of a circle which is obtained when a circle is divided evenly into four sections or rather 4 quadrants by a set of two lines which are perpendicular in nature.

Each of the four sections is called a quadrant. When four such quadrants are joined, the structure that we get is nothing but a circle.

Fig 1. A circle with a quadrant ABOQuadrant

In the above figure (Fig 1.), we can see a circle with one of the quadrants ABO colored in green color and angle AOB makes a right angle (90) at the center O.

How to calculate the area of a quadrant?Quadrant To calculate the area of a quadrant of a circle, we must know the area of a circle.

To find the area of a circle C, we need to know the following.

  1. Center: a point O of a circle from where all other points are equidistant.
  1. Radius: is defined as length of a line segment R from the center point O

to anywhere on the perimeter of the circle.

  1. Diameter: is defined as a line segment D twice as the length of the

radius R. That is, D=2R

  1. Circumference is defined as the distance Ci around the edge of a circle C.

Fig 2. Area of a circle C

That is, Ci = 2Π, where Π= 3.14159.

  1. The area is defined as the number of square units contained inside the circle,

that is, pi (Π) multiplied by radius squared (r2).

Therefore, area of a circle, A=П*r2

Now, to calculate the area of a quadrant, divide the area of a circle by 4 (as four quadrants make a circle). We get,

Area of a quadrant, A=  (П*r2)/4.

Let us see one example. Find the area of a quadrant Q of a circle C with radius 8 cm.

Solution: Given,

Radius, R=8 cm

Area of circle= П*r2

= 3.142 * 8 * 8

= 201.088 cm2

Now, to calculate the area of a quadrant Q of the circle C, divide the area of the circle by 4.

Area of quadrant, A1 = area of circle / 4

= 201.088 / 4

= 50.272 cm2

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