Jar Lid

The diamaeter of the jar lid is 5.4 cm. What is the area of the top of the lid?

This is my sixth grade math homework and I really need help. It has to do with area and stuff like that.

First I want you to imagine you have a square.

Or, change imagination into reality and draw a square on a piece of paper.

Next draw a circle inside the square so that the circle touches the square at the very top, bottom, left and right edges.

To calculate the area of the square you would measure one side of the square and multiply it by itself. If the bottom edge of the square was 10, then the area of the square would be:
10x10 = 100

When you multiply something by itself, you know what that is, right?

We say it is "squared".

Now put a dot in the very center of the circle.

If the bottom edge of the square were ten, then from the center dot to the right side of the square would be exactly half = five and from the center dot to the left would also be half of ten and also = five.. That is because the center dot is in the middle of a line measuring ten. A line of length ten which is divided in half, will , of course, become two shorter lines each equaling five.

Now, if you draw a line from the center dot straight down to the edge, it should hit at the same spot were the circle hit the bottom edge. Next draw a line from the center dot to the top edge, to the left, and to the right.

You should now have one big square which is 10 on each side. Inside the big square you have a circle which just barely touches the square at the top, bottom, left and right edges. And you have now drawn four lines inside the big square so that you have four small squares inside the big square: one square in the lower right, another in the lower left, a third in the upper left, and finally a fourth smaller square in the upper right.

If you want to calculate the area of one of these smaller squares, that would be the length of the side of the smaller square (5) multiplied by itself: 5x5=25

This makes sense because there are four squares and the total area of the big square is 10x10=100 and 25x4=100

YES, WHAT ABOUT THE CIRCLE???
(you are probably asking)

I'm getting to that...

The RADIUS of the circle is the distance from the center of the circle to the edge. The RADIUS is often abbreviated to just "R" or "r". The radius of the circle in our diagram is the same as the side of the smaller square. It is 5.

And we know that the area of the smaller square is 5x5=25.

But the outside corners of the smaller square are not part of area inside the circle.

We know the area of the big square is:

The area of the small square (5x5=25) times 4 = 100

But to know the area of the CIRCLE, instead of multiplying the area of the small square by 4, we need to multiply it by some number less than four to account for the part of the area inside the square that is not part of area inside the circle.

That special number is "pi"

Pi = approximately 3.14

If you multiply the area of the small square by 4 you get the area of the big square.

If you multiply the small square by pi (3.14) you will get the area of the circle!

By the way, diameter is the distance all the way across the middle of the circle. Diameter in my example is 10 and the radius is 5.

The diameter in your example was 5.4cm. That means the RADIUS is...

Come on...

5.4 divided in half = .......

2.7

That would make 2.7 the length of the side of the small square and also the radius of the circle. Look at your diagram, the side of the small square and the radius of the circle are the same.

And so to get the area of the small square you multiply the length of it's side by itself (squared):

2.7x2.7 = 7.29

That would be the area of the small square.

Then multiply the are of the small square by "pi" (3.14)

7.29 x 3.14 = 22.89 square centimeters

There is your answer.

This formula is usually written as:

Radius squared multiplied by pi. Then somebody thought it sounded cool to put pi in front and just call Radius "r" and to skip saying "times" or "multiplied by" because all those math geniuses are supposed to already know it, so they say "pi r squared" and they say it really fast so it sounds almost like "Pirate Square". So if you see some kid with thick glasses say "Pirate Square", you will know it is really "pi times r squared" and just tell him not to talk so fast.

Here is a question for you...

Now that you understand the area of a circle, can you tell me how to find the circumference?

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