Welcome to our Area of 1/4 Circle Support page.

We explain how to find the area of one-quarter of a circle and provide a quick calculator to work it out for you, step-by-step.

We also have several worksheeets and worked examples to help you practice and learn this skill.

The area of ¼ of a circle is equal to ¼ of the area of the whole circle.

- Select if you want to use the radius or diameter (default is radius).
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).

- Choose your units of measurement (default is cm)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Area button
- You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.

The sector of the circle shown is a ¼ circle.

The area of ¼ circle is equal to ¼ of the area of the whole circle.

So the area of the sector is:

\[ A = {1 \over 4} \pi r^2 \]

where A is the area of the sector, and r is the radius of the circle

We know that the radius is 8 cm, so we if we input this value into the formula, we get:

\[ A = {1 \over 4} \pi (8)^2 \]

We need to work out the brackets first.

\[ (8)^2 = 8 \times 8 = 64 \]

This gives us:

\[ A = {1 \over 4} \pi (64) \]

If we multiply the ¼ by 64 we get:

\[ A = 16 \pi \]

So this gives us:

\[ A = 50.3 \; cm^2 \; to \; 1\; decimal \; place \]

The sector shown is a ¼ circle.

The area of ¼ circle is equal to ¼ of the area of the whole circle.

So the area of the sector is:

\[ A = {1 \over 4} \pi r^2 \]

where A is the area of the sector, and r is the radius of the circle

We know that the radius is 4 ½ inches, so we if we input this value into the formula, we get:

\[ A = {1 \over 4} \pi (4 {1 \over 2})^2 \]

We need to work out the brackets first.

\[ (4 {1 \over 2})^2 = 4 {1 \over 2} \times 4 {1 \over 2} = {81 \over 4} \]

This gives us:

\[ A = {1 \over 4} \pi ({81 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {81 \over 16} \pi \]

So this gives us:

\[ A = 15.90 \; in^2 \; to \; 2\; decimal \; places \]

Each flowerbed is shown is a ¼ circle.

So the area of each flowerbed is:

\[ A = {1 \over 4} \pi r^2 \]

The radius of the circle is not shown, but we can see that the diameter of the circle (the distance from one side to the other) is equal to 15 m.

The radius is equal to half of the diameter, so:

\[ r = {d \over 2} = {15 \over 2} m \]

If we input this value into the formula, we get:

\[ A = {1 \over 4} \pi ({15 \over 2})^2 \]

We need to work out the brackets first.

\[ ({15 \over 2})^2 = {15 \over 2} \times {15 \over 2} = {225 \over 4} \]

This gives us:

\[ A = {1 \over 4} \pi ({225 \over 4}) \]

If we multiply the fractions gives us:

\[ A = {225 \over 16} \pi \]

Multiplying this fraction by π gives us:

\[ A = 44.2 \; m^2 \; to \; 1\; decimal \; place \]

We have created two worksheets for you to practice the skills shown on this page.

Take a look at some more of our worksheets similar to these.

We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.

Each calculator page comes with worked examples, formulas and practice worksheets.

We have a range of other area worksheets and support pages for a range of different 2d shapes.

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

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