Formula for Area of circle
The formula to find a circle's area $$ \pi $$ (radius)^{2} usually expressed as $$ \pi \cdot r^2 $$ where r is the radius of a circle.
The area of a circle is all the space inside a circle's circumference.
In the picture on the left, the area of the circle is the part of the circle that is changing color.
Explore and discover the relationship between the area formula , the radius of a circle and its graph with with our interactive applet
Practice Problems
Remember the Formula:
$$ Area = \pi \cdot r^2 \\ A = \pi \cdot ( 22')^2 \\ A = \pi \cdot 1,520 \text{ square feet} \\ A = 4775.220833456486\text{ square feet} \\ Area = \boxed{ 4775.2 } $$
Remember the Formula:
$$ Area = \pi \cdot r^2 \\ A = \pi \cdot ( 5")^2 \\ A = \pi \cdot 25 \text{ square inches} \\ A = 78.53981633974483 \text{square inches} \\ A = 78.5 \text{ square inches, rounded to nearest tenth} $$
Remember the Formula:
$$ Area = \pi \cdot r^2 \\ A = \pi \cdot (7 \text{ centimeters} )^2 \\ A = 153.93804002589985 \text{ square centimeters} \\ \boxed { A = 153.94 \text{ square centimeters, rounded to nearest hundredth}} \\ $$
Use the area formula ... but this time solve the radius
$$ A = \pi r^2 \\ 120 = \pi r^2 \\ \frac{120}{\pi} = r^2 \\ 38.197 = r^2 \\ \sqrt{38.197} = r \\ \boxed {r=6.18 \text{ inches }} $$
Like the last problem, we are given area and need to solve for radius ; However, this time, we need to then do one more step  find the diameter
$$ A = \pi r^2 \\ 360 in^2= \pi r^2 \\ \frac{360}{\pi} = r^2 \\ 114.59155902616465= r^2 \\ \sqrt{114.59155902616465} = r \\ r=10.704744696916627 \text{ inches } \\ $$
Now, that we have found the radius, how do we find the diameter?
$$ diameter = 2 \cdot radius \\ = 2 \cdot 10.704744696916627 \\ =21.409489393833255 \\ \boxed{diameter =21.41 \text{ inches, rounded to nearest hundredth}} $$
Divide Diameter in half to calculate radius:
Radius = $$ \frac{diameter}{2} = \frac{12}{2}= 6 $$
$$ A= \pi \cdot r^2 \\ A = \pi \cdot 6^2 \\ A = 36 \pi $$
Since the formula for the area of a circle squares the radius , the area of the larger circle is always 4 (or 2^{2}) times the smaller circle. Think about it: You are doubling a number (which means ×2) and then squaring this (ie squaring 2) which leads to a new area that is four times the smaller one.
You can see this relationship is true if you pick some actual values for the radius of a circle.
For instance, let's make the original radius = 3 .Smaller Circle  Larger Circle 

radius $$ =3 $$  radius = $$3 \cdot 2 =6 $$ 
A = $$ \pi (3)^2 $$  A = $$ \pi (6)^2 $$ 
A = $$ 9 \pi $$  A = $$ 36 \pi $$ 
This relationship holds true no matter what radius you pick
Let's make the original radius = 5 .
Smaller Circle  Larger Circle 

radius $$ =5$$  radius $$ =5 \cdot 2= 10$$ 
A = $$ \pi (5)^2 $$  A = $$ \pi (10)^2 $$ 
A = $$ 25 \pi $$  A = $$ 100 \pi $$ 

This page:
 Formula for area of circle

Related Pages:
 Mixed Practice(area, circumference)
 standard form equation for a circle
 arc
 chord
 circumference
 intersection of chords within circle
 interactive applet