Creating rectangles with a given area 1

- [Voiceover] Each small square on the grid has an area of one square unit. So, each of these small squares is one square unit. This square is one square unit, and this square is one square unit, and so on. And now we're asked to draw a rectangle with an area of 10 square units. Well, this word "area" here is talking about how much space our shape covers. So, our shape in this case is a rectangle, so we're being asked to draw a rectangle that covers 10 square units, and we know that each of these is one square unit, so we want a rectangle that covers 10 of the square units. We could try just drawing a rectangle right across this top row until we get 10 square units, but the problem there is there's only one, two, three, four, five, six, seven square units going across the top. So we can't just do one long row of 10 square units. We can't do one long column either, because one, two, three, four, five, six. Only six square units, so we can't draw a rectangle going down like that either because we need 10 square units. So that means we're gonna have to break up our 10 into equal groups. Since it can't all fit on one row, we're gonna have to break up the unit squares into groups. So, we can break up a 10 into two groups of five, or five groups of two. Either one of those will work. So let's do that. Let's draw ourselves a rectangle, and we'll start up here. Here's a rectangle. And let's see, that's five. And we can space and make sure that covers the whole square unit. There we go. So here's our rectangle, and this rectangle covers one, two, three, four, five, there's the first row of five. And the second row of five has unit squares six, seven, eight, nine, and ten. So, here's one perfect answer, a rectangle that has two rows of five square units, and we could've drawn this rectangle anywhere on the grid. It doesn't matter. We could've drawn it down here with two rows of five, or right here with two rows of five. Any rectangle covering two rows of five has an area of 10 unit squares. Similarly, any rectangle covering five rows of two, let's look and see if we can try to show that. Here we go. Here's a rectangle. And this one will cover one, two, so we have rows of two, and there's five rows. So, one, two, three, four, five, six, seven, eight, nine, 10. So again, this rectangle covers 10 square units. So any rectangle you can draw on the grid that either covers two rows of five square units or five rows of two square units is a rectangle with an area of 10 square units.