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# Area of a circle formulas

## Common Core Standard: 7.G.4 7th Grade Math

### Area and Perimeter Formulas

The area of a circle is the total number of square units found in the space inside the circle. You could count all of the squares inside the circle, but it is much easier and more accurate to use the formulas for finding the area of a circle.

In order to calculate the area of a circle you will need one of these measures.

Radius which the distance from the center of the circle to the edge.

Diameter which is the distance across the circle and through the center. The diameter is twice the length of the radius. of the circleacross the circle.

​Circumference is the distance around a circle.  π is ratio of a circles using circumference divided by it’s diameter.

There are several formulas for finding the area of a circle based on information provided.

If the radius is given use,

If diameter is given use,

If circumference is given use a two step process.
Step 1. Find the radius from the circumference using,
Radius = circumference/ π

Step 2. After finding the a radius, use the formula,

## Finding the area of a circle step by step.

Find the area of a circle with a radius of 4 units.

Plug your given information into the area of circle formula:

π * 4*4 = π16 units squared is the exact answer
3.14* 16 = 50.24 units squared is an approximate answer.

Find the area of a circle with a radius of 8 units.
π * 8*8 = π64
3.14* 64   ≈ 200.96 units squared
Find the area of a circle given a diameter of 10 units.
Given the diameter you could find the area two ways.
Option 1.  Use the formula,
3.14/4 = .785
Square the diameter, 10 squared = 100
.785 * 100 ≈ 78.5 units squared

Option 2
Divide diameter by 2 in order to find the radius
10/2 = 5
Then use,
π * r*r
π * 5*5 = π25
3.14 * 25 ≈ 78.5 units squared

## Find the area of a circle using circumference.

Find the area of a circle with a circumference of 20 π units.

Step 1. Find the radius of the circle using Circumference = 2 πr
20 π = 2 πr
Divide each side by π
20 π/ π= 2 πr/ π
20= 2r
Divide by 2 both sides
20/2 = 2r/2

Step 2. Now plug the radius of 10 into the area formula.
Area = π* 10 *10 = 100 π  or 3.14*100 ≈ 314 units squared

### Find the radius of a circle that has an area of 81π inches ^2

What do you do if you know the area of a circle, and want to know the radius?

Step 1. In order to find the radius you will work backwards. Plug your given information into the formula,  Area = πr^2
πr^2 = 81

Step 2. Divide each side by π
πr^2/π = 81/π

Step 3. Take the square root of both sides
√r^2 = √81

Step 4. Solution = r =9

Common Core Standard: 7.G.4 Seventh Grade Geometry (7.G) Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.