# How do you find the area of a circle?

Lets go over how you would find out the area of a circle of any size using a few different methods. Since we all like to do things the way we understand best, I’ll give you a few choices and you can use the way that best suits your learning style.

## VOCABULARY

Like in the  shapes lesson, we learned some vocabulary about different shapes. I am going to quickly go through them and how they apply to circles:

AREA - Area is the sum total of the space taken up by an object or in this case a shape. Each shape has a different method to learn the area of it

CIRCUMFERENCE - This is the measured length of distance around the outside edge of a shape, mostly this refers to the edge of a rounded shape like a circle or ellipse.

RADIUS - Radius is the distance from the center of a circle to the outer edge

DIAMETER - Diameter is the distance from one edge of a shape to the other, bisecting the shape evenly in half. In most cases, the dividing line MUST go through the center point of the shape.

PI (π) - PI is the relational measurement between the radius and the diameter of a circle. This measurement is crucial to finding the area of a circle. The aproximate measurement is 3.14159265359 or simply 3.14 (if anything else about PI, remember 3.14!!)

## Calculating Area of a Circle

Area of a circle is the radius of the circle squared times PI or  A = π(r²)

Remember that the units for the answer will be squared!!  (ie.   in²  or  yd² )

### Examples when radius is known:

2. * 3.14

 Radius = 5.3 in Radius = 2.5 yd Radius = 5.7 yd Radius = 4.8 ft Solve A=π * r² 1. 5.3 * 5.3 = 28.09 2. 28.09 * 3.14 = 88.20 3. 88.2 in² Solve A=π * r² 1. 2.5 * 2.5 = 6.25 2. 6.25 * 3.14 =19.62 3. 19.6 yd² Solve A=π * r² 1. 5.7 * 5.7 = 32.49 2. 32.49 * 3.14 = 102.01 3. 102 yd² Solve A=π * r² 1. 4.8 * 4.8 = 23.04 2. 23.04 * 3.14 = 72.34 3. 72.3 ft²

## Examples when diameter is known:

[Hint - Remember that Diameter = Radius * 2   or   Radius = Diameter / 2]

2. * 3.14

 Diameter = 1.0yd Diameter = 24 in Diameter = 16yd Diameter = 48 ft Solve A=π * r² Radius = 1.0 / 2 = 0.5 1. 0.5 * 0.5 = .25 2. .25 * 3.14 = 0.785 3. 0.785 yd² Solve A=π * r² Radius = 24 / 2 = 12 1. 12 * 12 = 144 2. 144 * 3.14 = 452.16 3. 452.2 in² Solve A=π * r² Radius = 16 / 2 = 8 1. 8 * 8 =  64 2. 64 * 3.14 = 200.96 3 201 yd² Solve A=π * r² Radius = 48 / 2 = 24 1. 24 * 24 = 576 2. 576 * 3.14 = 1808.64 3. 1808.6 ft²

## STRATEGIES

Solving area of circle problems just requires you to see what information is given and then solve for what the question is asking for. Be very careful to see what the question is asking for and the answers. If you are solving for area &  if you don’t see an answer that has the units squared (in²), there may be a good chance that is an incorrect answer. Always understand what you are solving for and then select the BEST answer.

## AREA OF CIRCLES RECAP

• AREA OF CIRCLE = π * r²
• PI or π = 3.14
• RADIUS is the measurement from center of circle to outside edge
• DIAMETER is the measurement across the middle of circle, bisecting the center
• DIAMETER = RADIUS * 2
• Be sure to follow Order of Operation

If you have any questions please comment and good luck on your studying for the ASVAB exam!