Lesson 2: Area of a Circle

Property

The area of a circle represents the total flat space enclosed inside it. The formula is:

(where r is the radius, and $\pi$ is approximately 3.14 or 22/7)

Examples

• A circular pizza has a radius of 8 inches. Its area is $A = \pi(8^2) = 64\pi$ square inches, which is about 201 square inches.
• A clock has a radius of 5 cm. Its area is $A = \pi(5^2) = 25\pi$ square cm.

Explanation

Why is the formula $\pi r^2$? Imagine cutting a circle into tiny, equal pie slices. If you arrange them alternating up and down, they form a shape that looks like a parallelogram!
The height of this parallelogram is just the radius of the circle (r). The base is exactly half of the circle's outside edge (half the circumference, which is $\pi r$). Just like a regular parallelogram, Area = base x height. So, $\pi r \times r$ gives us the magical $\pi r^2$!

Property

The area formula

Examples

• Circle with diameter 10 cm: First, find the radius (10 / 2 = 5 cm). Then, $A = \pi(5^2) = 25\pi$ square cm.
• Circle with diameter 14 inches: First, find the radius (14 / 2 = 7 inches). Then, $A = \pi(7^2) = 49\pi$ square inches.
• Circle with diameter 6.8 meters: Radius is 3.4 meters. $A = \pi(3.4^2) = 11.56\pi$ square meters.

Explanation

This is the most common mistake in geometry! Since the diameter is twice as long as the radius, if you accidentally plug the full diameter into the $A = \pi r^2$ formula, your final answer won't just be double—it will be FOUR times too big! Always ask yourself: "Did they give me the full slice across, or just from the center?" If it's the full slice, chop it in half first.