100:00:00,269 --> 00:00:03,823I have two identical rectangles here,

200:00:03,823 --> 00:00:05,935and I want to measure how much each of them,

300:00:05,935 --> 00:00:05,936or how much space each of them takes up on the plane of my screen; The screen you are looking at right now.

400:00:05,994 --> 00:00:14,937And I want to do it using two different units.

500:00:14,937 --> 00:00:19,544It is clear since they are two identical rectangles that they take up the exact, same amount of space.

600:00:19,544 --> 00:00:22,210They will have the same area.

700:00:22,210 --> 00:00:25,627But what we can see is that we can measure that area using different units.

800:00:25,627 --> 00:00:31,804So, first over here. Let's say, this figure is one foot in width.

900:00:31,804 --> 00:00:38,070So, let's say that, it is one foot in width. So that is, one foot in width.

1000:00:38,070 --> 00:00:42,470And, it is also one foot in height. One foot in height.

1100:00:42,470 --> 00:00:51,544So, this right over here is equal to one square foot. It is clearly a square, it has the same width and the same height.

1200:00:51,544 --> 00:00:55,044And each of these dimensions are one foot. So, we can call it 'one square foot'.

1300:00:55,044 --> 00:00:59,627So, let's see how many square feet we can get on to one of these rectangles.

1400:00:59,627 --> 00:01:03,210Essentially, what we will be measuring its area in terms of square feet.

1500:01:03,210 --> 00:01:07,961And, so we want to cover the entire space without overlapping, and without going over the boundaries.

1600:01:07,961 --> 00:01:24,044So, that is: One...Two...Three...Four...Five...and Six.

1700:01:24,044 --> 00:01:39,877Six in that first row. And then I have: Seven...Eight...Nine...Ten...Eleven...and Twelve.

1800:01:39,877 --> 00:01:46,803So that looks like this area, which is the same as this area down here, if I were to measure in square feet it is equal to...

1900:01:46,803 --> 00:02:02,210The area is equal to (let me write this down)...The area is equal to, we have (let me write it down): One...Two...Three...Four...Five...Six...Seven...Eight...Nine...Ten...Eleven...Twelve

2000:02:02,210 --> 00:02:04,403square feet.

2100:02:04,403 --> 00:02:07,73612 square feet.

2200:02:07,736 --> 00:02:12,127Now, I am going to try to measure that same area in a different unit.

2300:02:12,127 --> 00:02:14,270And I am going to make-up this unit.

2400:02:14,270 --> 00:02:16,136I am going to call it a: "Furgle."

2500:02:16,136 --> 00:02:19,137And a "Furgle" in one-dimension is twice a foot. And this (that) distance over here I am going to call a: "Furgle."

2600:02:19,137 --> 00:02:29,711That is one "furgle." This is something that I made up just for the purposes of this video.

2700:02:29,711 --> 00:02:32,336Most people will not recognize what a furgle is.

2800:02:32,336 --> 00:02:35,870So, its height is one "furgle" and its width is one "furgle."

2900:02:35,870 --> 00:02:42,403And so we can say that this is, one square "furgle."

3000:02:42,403 --> 00:02:51,544One square "furgle." So, let's see how many square "furgles" is this area. That same area that is 12 square feet.

3100:02:51,544 --> 00:03:01,127So, let me copy and paste this. So, let me, copy...and then paste.

3200:03:01,127 --> 00:03:04,877So let's see, we can get one square"furgle" on there,

3300:03:04,877 --> 00:03:07,403another square furgle on there

3400:03:07,403 --> 00:03:12,470and we can get a third square "furgle" on there!

3500:03:12,470 --> 00:03:15,293So, we get one...two...three square furgles.

3600:03:15,293 --> 00:03:28,003The area of this figure in "furgles," square "furgles" I should say: The area is three square "furgles."

3700:03:28,003 --> 00:03:34,960So it's the same exact area. Three square "furgles" is equal to twelve square feet.

3800:03:34,960 --> 00:03:37,128Covering the exact same area.

3900:03:37,128 --> 00:03:38,710And, what I encourage you to think about is:

4000:03:38,710 --> 00:03:42,710How many square feet make a square "furgle"?