# Area of 3/4 Circle Support

Welcome to our Area of 3/4 Circle Support page.

We explain how to find the area of three quarters 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.

### Area of a 3/4 Circle Calculator

Area of a 3/4 Circle Calculator

### Area of 3/4 Circle Examples

#### Example 1) Find the area of the sector below, giving your answer to 1 decimal place: The sector of the circle shown is a ¾ circle.

The area of ¾ circle is equal to ¾ of the area of the whole circle.

So the area of the sector is:

$A = {3 \over 4} \pi r^2$

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

We know that the radius is 3cm, so we if we input this value into the formula, we get:

$A = {3 \over 4} \pi (3)^2$

We need to work out the brackets first.

$(3)^2 = 3 \times 3 = 9$

This gives us:

$A = {3 \over 4} \pi (9)$

If we multiply the ¾ by 9 we get:

$A = {27 \over 4} \pi$

Multiplying this fraction by π gives us:

$A = 21.2 \; cm^2 \; to \; 1\; decimal \; place$

#### Example 2) Work out the area of the circular grass sector below, giving your answer to 2 decimal places. The area of ¾ circle is equal to ¾ of the area of the whole circle.

So the area of the sector is:

$A = {3 \over 4} \pi r^2$

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

We know that the radius is 5 ½ meters, so we if we input this value into the formula, we get:

$A = {3 \over 4} \pi (5 {1 \over 2})^2$

We need to work out the brackets first.

$(5 {1 \over 2})^2 = 5 {1 \over 2} \times 5 {1 \over 2} = {121 \over 4}$

This gives us:

$A = {3 \over 4} \pi ({121 \over 4})$

If we multiply the fractions gives us:

$A = {363 \over 16} \pi$

Multiplying this fraction by π gives us:

$A = 71.27 \; m^2 \; to \; 2\; decimal \; places$

#### Example 3) Tyger makes a yellow logo for a T-shirt design shown below. Find the area of the yellow logo to 1dp. The sector of the circle shown is a ¾ circle.

So the area of the sector is:

$A = {3 \over 4} \pi r^2$

The radius of the circle is not shown, but we can see that the diameter (the distance from one side to the other) is equal to 7 inches.

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

$r = {d \over 2} = {7 \over 2} inches$

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

$A = {3 \over 4} \pi ({7 \over 2})^2$

We need to work out the brackets first.

$({7 \over 2})^2 = {7 \over 2} \times {7 \over 2} = {49 \over 4}$

This gives us:

$A = {3 \over 4} \pi ({49 \over 4})$

If we multiply the fractions gives us:

$A = {147 \over 16} \pi$

Multiplying this fraction by π gives us:

$A = 28.9 \; in^2 \; to \; 1\; decimal \; place$

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