## What is Quadrant?

A quadrant is a term used to refer to one of the four sections or quarters of a plane or space that is divided by two intersecting lines. A quadrant is typically used in a Cartesian coordinate system. It is a coordinate system that uses two perpendicular axes to locate points in a plane or space.

The two axes are usually labeled **the x-axis **and **the y-axis**. The intersection of the two axes is called the **origin**, and it is located at (0,0). The four quadrants in a Cartesian coordinate system are usually labeled with Roman numerals as follows:

**Quadrant I:**This quadrant is located in the**upper right-hand corner**of the plane. It contains all points with positive x-coordinates and positive y-coordinates.**Quadrant II:**This quadrant is located in the**upper left-hand corner**of the plane. It contains all points with negative x-coordinates and positive y-coordinates.**Quadrant III:**This quadrant is located in the**lower left-hand corner**of the plane. It contains all points with negative x-coordinates and negative y-coordinates.**Quadrant IV:**This quadrant is located in the**lower right-hand corner**of the plane. It contains all points with positive x-coordinates and negative y-coordinates.

## Area Of Quadrant

The area of a quadrant depends on the radius of the circle that the quadrant is a part of.

**Area of quadrant = (1/4) × π × r ^{2}**

Where:

- “r” is the radius of the circle and
- “π” is the mathematical constant pi, approximately equal to 3.14.

## How to Calculate the Area of a Quadrant?

To calculate the area of a quadrant, you need to use the following formula:

Area of quadrant = (1/4) x π x **r ^{2}**

To use the formula, follow these steps:

- Measure the radius of the circle.
- Square the radius by multiplying it by itself.
- Multiply the squared radius by π (3.14).
- Divide the result by 4 to find the area of the quadrant.

**For example, if the radius of the circle is 10 cm, then the area of the quadrant.**

Area of quadrant = (1/4) x π x**r ^{2}**

= (1/4) x 3.14 x 10^{2}

= (1/4) x 3.14 x 100

Area of quadrant = 78.5 square centimeters

### Area of a Quadrant Examples

**Example 1: Find the area of a quadrant with a radius of 5 cm.**

**Solution:**

Area of quadrant = (1/4) x π x **r ^{2}**

Area of quadrant = (1/4) x 3.14 x 5

^{2}= (1/4) x 3.14 x 25

Area of quadrant = 19.63 square centimeters

Therefore, the area of the quadrant is 19.63 square centimeters.

**Example 2: Find the area of a quadrant with a radius of 8 cm.**

**Solution:**

Area of quadrant = (1/4) x π x **r ^{2}**

= (1/4) x 3.14 x 8

^{2}Area of quadrant = (1/4) x 3.14 x 64

Area of quadrant = 50.27 square centimeters

Therefore, the area of the quadrant is 50.27 square centimeters.

**Example 3: Find the area of a quadrant with a radius of 12.5 cm.**

**Solution**:

Area of quadrant = (1/4) x π x**r ^{2}**

Area of quadrant = (1/4) x 3.14 x 12.5

^{2}= (1/4) x 3.14 x 156.25

Area of quadrant = 122.72 square centimeters

Therefore, the area of the quadrant is 122.72 square centimeters.

## Frequently Asked Questions on Area of Quadrant

**Q: What is a quadrant?**

A: A quadrant is one-fourth of a circle. It is formed by dividing a circle into four equal parts.

**Q: What is the difference between a quadrant and a sector?**

A: A quadrant is one-fourth of a circle, while a sector is a portion of a circle that is bounded by two radii and an arc.

**Q: Can the area of a quadrant be negative?**

A: No, the area of a quadrant cannot be negative. The area of any shape is always a positive value.

**Q: How do you find the perimeter of a quadrant?**

A: The perimeter of a quadrant is the sum of the length of the curved edge and the two radii. The formula for the perimeter of a quadrant is: Perimeter of quadrant = 1/2 x 2πr + 2r, where r is the radius of the circle.

**Q: Can the area of a quadrant be greater than the area of a circle?**

A: No, the area of a quadrant cannot be greater than the area of a circle.