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 ABO
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?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.
- Center: a point O of a circle from where all other points are equidistant.
- Radius: is defined as length of a line segment R from the center point O
to anywhere on the perimeter of the circle.
- Diameter: is defined as a line segment D twice as the length of the
radius R. That is, D=2R
- 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.
- 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.
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