Finding missing side when given area | Math | 3rd grade | Khan Academy

The picture has an area of 80 square cm. What is the width of the picture?

So here's our picture: this super fun giraffe listening to music. Our picture's shape is a rectangle, and we're asked to find the width of that rectangle.

Well, maybe we don't know a special formula or a special equation to find the width, but we do know one to find the area of a rectangle. So let's use that formula and see how it can help us.

We know that the area of a rectangle can be found by multiplying the length of the rectangle over here—the length times the width. So if we multiply the two side lengths of a rectangle, we get its area.

In this picture, and this rectangle, we are told that our area is 80 square cm. So we already know the area, and we can use that to help us. We also know the length; we're told that this distance from here to here, this length, is 10 cm.

So the length is 10 times the width. We don't know the width, that's what we're looking for. What we do know, though, is that we need our width to be a number that when it's multiplied by 10, we get 80 for an answer.

So what number times 10 equals 80? It's 8. 8 times 10 equals 80. So that means the width of our picture is 8 cm.

Let's try one more: a rectangle has an area of 24 square m. The width of the rectangle is 4 m. What is the length of the rectangle?

So this time we don't even have a picture to look at, but we have enough information up here to solve this. Again, we can use our formula that tells us the area of a rectangle is the length times the width.

Now, we could draw this rectangle, it might be helpful to visualize it, but I'm going to show you here we could actually solve it without ever even seeing the rectangle because we know the area is 24 square m.

So the space the rectangle covers is 24 square m, and the length—we don't know the length; we're asked what is the length—but we do know that the width is 4 m.

So our length has to be some number that when it's multiplied times 4, we get 24 for the answer. That number must be 6, because 6 times 4 equals 24.

So the length of our rectangle is 6, and in this case, we're talking about meters.