Creating rectangles with a given area 1 | Math | 3rd grade | Khan Academy

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.

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. We're being asked to draw a rectangle that covers 10 square units. 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 1, 2, 3, 4, 5, 6, 7 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 1, 2, 3, 4, 5, 6 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 going to have to break up our 10 into equal groups. Since it can't all fit on one row, we're going to have to break up the unit squares into groups. 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. We'll start up here. Here's a rectangle. And let's see, that's five, and we can space to make sure that covers the whole square unit. There we go! So here's our rectangle.

This rectangle covers 1, 2, 3, 4, 5. There's the first row, five. And the second row, five has unit squares 6, 7, 8, 9, and 10. So, here's one perfect answer: a rectangle that has two rows of five square units.

We could have drawn this rectangle anywhere on the grid; it doesn't matter. We could have 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've rows of two and there's five rows. So, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So again, this rectangle covers 10 square units. So, any rectangle that 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.