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## 8th grade foundations (Eureka Math/EngageNY)

### Course: 8th grade foundations (Eureka Math/EngageNY) > Unit 7

Lesson 3: Topic D: Foundations# Area of a circle

This was made for a hackathon back in 2014!

## What is the area of a circle?

Unlike squares or rectangles, circles don't have any straight sides. If you draw a circle on graph paper, you'll find that it's hard to get an exact measurement - there are a lot of grid squares that are partly inside the circle, and partly outside. It's not clear how to count them.

Instead, let's start by estimating the area of the circle first. Since calculating the area of a square is easy, we can estimate the area of a circle by comparing it to squares that are smaller and larger than it.

The area of the square on the left is 7, squared, equals, 49 and the area of the square on the right is 10, squared, equals, 100, so we know that the area of the circle must be between 49 and 100. That narrows it down a bit, but we still don't know exactly what the area is. How can we find out?

Let's try cutting up a circle to see if we can rearrange it into a more familiar shape. Look below - see how the four quarters of a circle can be fitted together? The slider controls how many sections we divide the circle into. Slide it to the right to see what happens when we increase that number!

## Want to join the conversation?

- How do I figure out what is the area of the circle?(5 votes)
- you do radius times radius and then multiply pi(2 votes)

- How do you find diameter and radius when area is given?(3 votes)
- How do I figure out what the area is?(1 vote)
- Halfway through it says, "But if we just want the width of the rectangle, we only want half of that length." Why do we only want half of that length?(2 votes)
- how to find the area of circle(2 votes)
- A=pi(r^2) Area = pi(radius squared) Use 3.14 for pi. Diameter=2r(1 vote)

- if you are given a circumference then how do you find the radius(1 vote)
- Circumference = pi(diameter) = pi(2 radius)

Use 3.14 as pi

In your case not enough data is given. What is the diameter of the circle?(0 votes)

- so what is the formula for area of square(0 votes)
- Can you tell me how to get the area of a circle(0 votes)
- Why are there kittens in the middle of everything? Just to distract us? :P(0 votes)
- No, see, kittens are small cats n the faces of cats are round, ie; circular in shape and the whiskers of the kitten are about half the length of it's face so the kittens are there to lest us practice circumference of circles by figuring out how fate the face of the kitten is. :P :D(0 votes)

- why was it called pi in the first place though(0 votes)
- because its called pi because it time it for you(0 votes)