Area of a Quadrant is defined as the one-fourth space of a circle as a Quadrant is the one-fourth part of a circle. A circle is defined as the locus of a considerable number of focuses that are equidistant from the inside of the circle. When a circle is partitioned equally by drawing two perpendicular diameters, it results in making four parts of a circle. Each Part of a circle is called a Quadrant. The Areas of all four quadrants of a circle are equal, and the sum of the areas of the four quadrants is again equal to the area of the circle.
In this article, we will learn what is a Quadrant, what is an Area of Quadrant, Area of Quadrant Formula, and solve some problems based on it. So Let's start learning about quadrants with a clear definition of the Area of Quadrant fundamental concept in mathematics.
Table of Content
What is Quadrant of a Circle?
A quadrant is one-fourth part of a circle. A Quadrant is defined as the region formed by two coordinate axes namely the x and y axes within a circle at a right angle. A circle is a 2-D closed shape that consists of multiple focuses that are equidistant from a fixed point on the inside of the shape. When a circle is divided into four equal parts it gives 4 quadrants. These regions may include positive and negative values of both coordinate axes. In terms of a circle, the quarter of a circle is known as a quadrant, which is a segment of 90-degree angle. Each divided quadrant is equal in size and at the midpoint of a circle or the center O, they all make a 90-degree right angle.
Definition of Quadrant
A Quadrant is defined as the region formed by two coordinate axes namely x and y axis passing through the center within a circle at a right angle. These regions may include positive and negative values of both coordinate axes. When a circle is divided into four equal parts it gives 4 quadrants.
What is Area of a Quadrant of Circle?
Area of a quadrant is the one-fourth of the area of a circle. It means that a quadrant of a circle occupies space equal to the one fourth of the total space occupied by a circle. It can be also said that area of quadrant is half of the area of the area of the semicircle. Thus to find the area of a quadrant of a circle we just need to divide the area of the circle of which quadrant is a part. Since, we know that a quadrant is surrounded by two radii and an arc, such that the two radii are perpendicular. Hence we can say that a quadrant is a sector whose central angle is 90°. Thus we can find the area of the using the area of quadrant formula by keeping the central angle to be 90°. Let's learn more about the formulas of Area of Quadrant.
Area of Quadrant Formula
A quadrant is known as one-forth part of a circle. So to find the area of a quadrant of a circle, we need to divide the area of circle by 4 parts to proportionate it to the area of the one-fourth part of the circle, to calculate area of quadrant.
We can calculate the Area of Quadrant using different methods such as using radius ,using diameter and using area of sector:
Area of Quadrant of Circle using Radius
We can calculate the quadrant of a circle by using Radius. We know that Area of Quadrant is directly proportional to the square of its radius:
Area of Quadrant = 1/4 (Area of Circle)
Area of Quadrant = 1/4 × π × r2
Where,
- "π" (pi) is a Constant equal to 22/7 or 3.14159
- "r" is radius of the circle.
Area of Quadrant of Circle using Diameter
We can calculate the quadrant of a circle by using the diameter of a circle, we know that radius is equal to the half of the diameter:
we know that radius is half of the diameter r = d/2.
Area of quadrant = 1/4 × π ×(d/2)2
Area of quadrant = 1/4 × π ×(d2/4)
Area of Quadrant = 1/16 × π × d2
Where,
- "π" (pi) is a Constant equal to 22/7 or 3.14159
- "d" is diameter of the circle.
Area of Quadrant of Circle using Area of sector
We can calculate the quadrant of a circle by using the area of sector of a circle, As we know that quadrant of circle is also a sector of the circle ,we can obtain the area of a quadrant.
Area of a sector of a circle = (θ/360°) × π × r2
In a Quadrant θ = 90°
Area of a quadrant = (90°/360°) × π × r2
Area of a quadrant = 1/4 × π × r2
Where,
- "π" (pi) is a Constant equal to 22/7 or 3.14159
- "r" is radius of the circle.
How to Find the Area of Quadrant?
Various steps required to find the area of the quadrant are given below:
Step 1: Mark the radius of the circle.
Step 2: Put the value of the radius in the formula Area = 1/4 × π × r², where r is the radius and π is the constant with a value of 3.14 (approx) value
Step 3: Obtained the answer in step 2 is the required area of the quadrant. It is measured in square units.
Also check,
Solved Examples on Area of Quadrant
Example 1: A large drum is in a circular shape. Its radius is 5 units. What is the area of quadrant?
Solution:
A large drum is in circular shape means it is similar to circle, so we can use circle formulae to calculate the area of the large drum.
given, r = 5 units, π = 3.14
Area of quadrant = 1/4 × π × r²
⇒ Area of quadrant = 3.14 × 5 × 5 / 4
⇒ Area of quadrant = 19.625 units
Thus, the area of the quadrant is 19.625 units.
Example 2: If the plate is in a circular shape and its diameter is 4 units. Calculate the area of quadrant?
Solution:
We know that plate is in circular shape, and its diameter = 4 units
π = 3.14
we know that radius is half of the diameter r=d/2.
Area of quadrant = 1/4 × π ×(d/2)²
⇒ Area of quadrant = (3.14 /4) × 4 × 4 /4
⇒ Area of quadrant = 3.14 units
Therefore, the area of quadrant of the plate is = 3.14 units
Example 3: If the circumference of the circle is 8 units. Calculate its area of quadrant.
Solution:
To Calculate the area of a quadrant when the circumference of the circle is given, we need to determine the radius of the circle first using the given circumference.
The formula for the circumference of a circle is C = 2πr,
where,
- C stands for circumference
- r stands for radius
Given, the circumference is 8 units, hence 8 = 2πr
To calculate radius r:
r = 8 / (2π)
r = 1.27 units
Area of quadrant = π x (1.27 units)2 / 4
⇒ Area of quadrant = 3.14 x 1.61 / 4
⇒ Area of quadrant=1.2 square units.
Therefore, the area of quadrant is 1.2 square units.
Example 4: Find the area of quadrant if the radius is 21 cm.
Solution:
given , Radius(r) = 21 cm
Now, Area of quadrant = 1/4 × π × r² cm square units
Area of quadrant = (22/7) × 21 × 21 /4
⇒ Area of quadrant = 235.93cm square units
⇒ Area of quadrant = 1386 cm2
Thus, Area of quadrant is 235.93cm square units
Example 5: Find the area of the quadrant of a circle if its radius is 14 cm.
Solution:
Given r = 14 cm, π = 22 / 7
Area of quadrant = 1/4 × π × r²
⇒ Area of quadrant = 22 / 7 × 14× 14/4
⇒ Area of quadrant = 154 cm2
Thus, the required area of quadrant = 154 cm2
Example 6: Calculate the area of quadrant by using the area of sector of a circle that subtends 60° angle at the center, and its radius is 14 cm.
Solution:
Given r = 14 cm, π = 22 / 7
Area of sector = (θ/360°) × πr2
⇒ Area of sector = (60° / 360°) × 22 / 7 × 14 x 14
⇒ Area of sector = 102.67 cm square units
⇒ Area of Quadrant = (1/4) × Area of Sector
Thus, the required area of quadrant = 25.66 cm square units
Practice Problems on Area of Quadrant
Problem 1: Given a circle shaped rope with a radius of 8 meters, find the area of quadrant.
Problem 2: If the circumference of the circle is 10 units. Calculate its area of quadrant.
Problem 3: Calculate the area of quadrant area of a sector of a circle with a central angle of 45 degrees and a radius of 6 inches.
Problem 4: Calculate the area of quadrant by using the area of sector of a circle that subtends 50° angle at the center, and its radius is 12 cm.
Problem 5: If the plate is in a circular shape and its diameter is 5 units. Calculate the area of quadrant?