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. In this article, let us discuss what is a quadrant, how to calculate the area of the quadrant with examples in detail.
What is Quadrant?
Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is an arc of 90 degrees. 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 colour and angle AOB makes a right angle (90) at the centre 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 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 centre 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
- The 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 the radius squared (r2).
Therefore, the area of a circle, A=Пr2
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= (Пr2)/4.
Area of a Quadrant Example
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 circle C, divide the area of the circle by 4.
Area of quadrant, A1 = area of circle / 4
= 201.088 / 4
= 50.272 cm2