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Area of Quadrant Formula
A circle is a closed curved shape with all points equidistant from a central point called the center. It is one of the fundamental shapes in geometry and has various properties, including its circumference, diameter, radius, and area.
A quadrant, on the other hand, is a specific section of a circle. It is formed by drawing two perpendicular lines that intersect at the center of the circle, dividing the circle into four equal parts. Each of these parts is a quadrant. In geometry, a quadrant covers 90 degrees of the circle’s total 360-degree angle.
The area of a quadrant is calculated using the formula (π * r²) / 4, where “r” represents the radius of the circle. This formula finds the area of one of the four equal sections created by the intersecting lines, or one-fourth of the total circle’s area. Quadrants are often used in geometry and trigonometry to calculate angles and areas in circular shapes.
What is Quadrant?
A quadrant is a subdivision of a plane. It is a four-sided figure with four right angles.
The coordinated frame system has four quarters or segments in it and these quarters or segments are known as the quadrants. These quadrants are all equal in size and area. With respect to a circle, the quarter of a circle is known as a quadrant, which is a segment of 90 degrees. Let us consider four such quadrants attached together. What does it make? It forms a circle. Let’s understand this better with the help of the image given below. You can see that the circle has been divided into four equal parts. Now, these parts are known as quadrants. Each of these quadrants is equal in size and at the midpoint or the center O, they all make a 90-degree right angle.
How to Calculate the Area of a Quadrant of Circle?
Before we go ahead and learn how to calculate the area of a quadrant of a circle, there are a few things you must know. Stated below are the key factors you must keep in handy before you solve the problem.
In order to find the area of a quadrant of a circle, you first need to know the area of the circle. Here’s a list of things you need to know.
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The Center of a Circle: All the points of the circle are at an equal distance from the center of the circle. Hence, this is known as the center.
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The Radius of a Circle: The distance from the center of the circle to any point on the circle, is known as the radius of the circle. It is denoted by the letter R.
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The Diameter of a Circle: The diameter is twice the radius of the circle. It is denoted by the letter D.
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The Circumference of a Circle: The distance around the edge of the circle is called the circumference of the circle.
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The formula of the circumference of Circle: Circumference = 2πr
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The Area of a Circle: The total amount of sq units occupied by a circle is known as the area of the circle.
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The formula of Area of Circle: Area = π x radius x radius or Area of circle = πr2
How to Calculate the Area of a Quadrant of Circle?
The area of a quadrant of a circle can be found by using the following equation: A = πr²
Methods to Calculate the Area of a Quadrant
There are a few ways to calculate the area of a quadrant. One way is to use the formula for the area of a triangle, which is one-half the base multiplied by the height. Another way is to use the formula for the area of a rectangle, which is the base multiplied by the height.
The Formula for The Perimeter of a Quadrant
The perimeter of a quadrant is the distance around the four sides of the quadrant. To find the perimeter of a quadrant, multiply the length of each side by 4.
Related Links:
- Area of Square
- Area of Triangles with 3 Sides
- Area of A Sector of A Circle
- Area of an Octagon
- Area of a Pentagon
- Area of Trapezium
- Area of a Prism
Frequently Asked Questions (FAQs) on Area of Quadrant
The formula for the area of a quadrant is (π * r²) / 4, where r is the radius of the circle.
To calculate the area of a quadrant, square the radius, multiply it by π (pi), and then divide by 4.
The formula represents the area of one-fourth of a circle, which is the area of a quadrant.
The area of a quadrant is used in geometry to find the space enclosed by a quarter-circle, helping in various calculations and applications.
No, the formula calculates the area of one-fourth of a circle. To find the area of the full circle, you would use the formula π * r².
The area of a quadrant increases with the square of the radius. As the radius grows, the area of the quadrant becomes larger.
The units for the area of a quadrant are determined by the units used for the radius. For example, if the radius is in meters, the area will be in square meters.
A quadrant is a quarter of a circle, and its area and angles are important for various calculations involving circular shapes and angles. What is the area of a quadrant formula?
How is the area of a quadrant calculated?
What does the formula (π * r²) / 4 represent?
Why is the area of a quadrant important?
Can the area of a quadrant be used for a full circle?
How does the radius affect the area of a quadrant?
What units are used for the area of a quadrant?
What is the significance of a quadrant in geometry?
