# How to Find the Area of a Quadrant (a Quarter of a Circle)

*Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.*

## What Is a Quadrant?

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Alternatively, you could substitute the radius of the quadrant directly into the formula A = ¼ πr². Let’s take a look at a few examples on working out the area of quadrants:

**Example 1 **

Work out the area of this quadrant (radius 8cm).

Method 1 (using the area of a whole circle and dividing by 4)

First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:

A = π ×r²

= π ×8²

= 64π (leave the answer as an exact solution as this need to be divided by 4).

So all you need to do now is divide the answer by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.

Method 2 (using ¼ πr²)

Substitute r = 8 directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 8².

A = 50.3 cm²

As you can see it gives exactly the same answer as method 1.

**Example 2**

Work out the area of this quadrant (radius 3.8m).

Like example 1, begin by substituting the radius of 3.8m into the formula for the area of the circle:

A = π ×r²

= π ×3.8²

= 14.44π (leave the answer as an exact solution as this need to be divided by 4).

Again, all you need to do now is divide the answer by 4:

Area of a quadrant = 14.44π ÷4 = 16π = 11.3 m² to 3 significant figures.

Method 2

Substitute r = 3.8m directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 3.8².

A = 11.3 m²

As you can see it gives exactly the same answer as method 1.

## Questions & Answers

**Question:** Can you find the area of quadrant of a circle whose circumference is 22?

**Answer:** First, find the radius of the circle by dividing the circumfernece by Pi and halving the answer to give 3.501 to 3 decimal places.

Now use 0.25*Pi*radius^2 to give the area of the quadrant 0.25*Pi*3.501^2 = 9.63 to 2 decimal places.

**Question:** If the area of a circle is 100 cm2, what's the area of one of its quadrants?

**Answer:** All you need to do is divide 100 by 4 to give 25 cm^2.

**Question:** If the wheel of a gate is 3 feet from the wall and it turns over 90 degrees, what is the distance covered by the wheel?

**Answer:** First double 3 feet to give a diameter of 6 feet.

Next multiply 3.14 by 6 to give the circumference of the whole circle which is 18.84 feet.

Now divide the answer by 4 as 90 degrees is 1/4 of the whole circle to give 4.7 feet to 1 decimal place.

**Question:** The radius of a quarter circle is 3 millimeters. What is the quarter circle's area? (r=3 mm, Pi = 3.14)

**Answer:** Work out 3^2 which is 9.

Now times 9 by 3.14 which is 28.26.

Now divide 28.26 by 4 to give 7.065 mm^2.

**Question:** What is the area of a quadrant with a radius of 6cm, given in terms of Pi?

**Answer:** First square the radius of 6 to give 36.

Now multiply 36 by Pi to give 36Pi

Next, divide the answer by 4 to 9Pi.

**Question:** What is the formula for working out the area of a quadrant?

**Answer:** 0.25*Pi*r^2.

**Question:** Is the area of a quarter-circle supposed to be (8² x π) /4 ?

**Answer:** Yes, the formula can be written as (radius² x π) /4.

I think you are showing an example when the radius of the quarter circle is 8.

**Question:** Can you find the area of a quadrant whose radius is 9cm?

**Answer:** Square 9 to give 81.

Now multiply 81 by 3.14 to give 254.34.

Finally divide 254.34 by 4 to give 63.6 to 1 decimal place.

**Question:** What is the area of the quadrant with a radius of 14cm ?

**Answer:** The area of the whole circle is Pi times 14 times 14 which gives 615.75... cm^2.

Now divide this answer by 4 to give 153.9 cm^2 to 1 decimal place (or 49Pi).

**Question:** What is the area of a quadrant with a radius of 4.3cm?

**Answer:** Work out 0.25 mutlplied by Pi multiplied by 4.3^2 to give 14.5 cm^2 rounded to 1 decimal place.

**Question:** What is the Area for 1/4 circle with radius of 6?

**Answer:** First square the radius to give 36, and multiply it by π to give 36π.

Now divide this answer by 4 to give 9π.

## Comments

**d,annalee** on September 08, 2013:

Not what i was looking for but good