# Circles: Area

The area of a shape is the size of the area inside the boundaries of that two-dimensional shape (once you start working with three dimensional shapes, area will refer to the two-dimensional area of one of the faces of that shape).

To find the area of a circle, you must find the radius of the circle. The radius is the distance from the middle of the circle to the edge (the radius is half of the diameter, which is the distance from side to side of a circle, through the center). Once you find the radius of the circle, you find the area of the circle by squaring the radius, and then multiplying it by $\pi$.

Units for area are always square units (e.g., square inches ($\text{in}^2$) or square feet ($\text{ft}^2$)).

*Example: *Find the area of the circle below.

The length of the radius is 3: $r=3$

$$\eqalign{\text{area}&=\text{radius}^2\times\pi\\a&=3^2\times\pi\\a&=9\pi \text{ units}^2\\&\text{Or}\\a&=9\pi\\a&=9\times 3.14\\a&=28.26 \text{ units}^2}$$

Special note about $\pi$. $\pi$, called "pi" is a constant that is often used with circles, and is an irrational number, which means that it is an decimal that never ends. We usually round it to $3.14$ or $\dfrac{22}{7}$.

The only hard part about finding the area of a circle is finding the radius. Then just square it and multiply it by $\pi$ and you have your area.

#### Practice Problems:

## Circles: Area

1. Find the area of a circle with a radius of 12 inches.

2. Find the area of a circle with a diameter of 8 inches.

3. Find the area of the circle:

4. Find the area of the circle:

5. If the area of a circle is $81\pi$ feet, what is the length of the radius?

6. Find the area of a circular amphitheater if the length across its center is 450 feet.

7. If a circular room has a radius of 25 feet, what is the area of the room?

8. If a circular field has a diameter of 30 feet, what is the area of the field?

9. If the area of a hot tub is 50.24 feet, how long is the radius of the hot tub?

10. If you need to paint a circular sign that has a diameter of 12 inches, what is the size of the area that needs to be covered in paint?

#### Answer Key: