Math 3: Finding Area and Perimeter with a Missing Number

Finding the area and perimeter of a rectangle was easy when we had all the rectangle's side measurements, but you didn't think it was going to stay that easy, did you? Come on, it's math. It's supposed to make you cry.

3rd GradeMath
Elementary and Middle School3rd Grade
LanguageEnglish Language

Transcript

00:26

The world will never know.

00:28

Anyway, sometimes when we're doing math related to areas and perimeters, we have to deal with [Teacher discussing area and perimeters in Math class]

00:32

missing numbers…

00:33

…but luckily there are tried and true ways of finding them.

00:35

So let's take a look at this rectangle.

00:38

To find its area, all we need to do is multiply its length by its width…[Area calculation beside a rectangle]

00:41

…so we'd multiply eight inches…

00:43

…by four inches…

00:44

…to find 32 square inches.

00:46

No sweat.

00:47

But what about this one?

00:49

Here we know the length of one side, and the area, but not the length of the other side. [Rectangle displaying the area and the length of one side but not the other side]

00:54

Is there any way to find the length of that missing side?

00:57

Do we need to put up missing posters on every lamppost in town? [Missing sign poster of a rectangles missing side length]

01:01

Nope!

01:02

Luckily for us – and for the posts – we just need to do some math.

01:05

Let's think back to the formula for the area of a rectangle: the area of a rectangle is [Rectangle with an area of 15 square inches]

01:09

equal to its length times its width.

01:11

We know that its area is fifteen square inches…

01:13

…and its length is five inches, so the width has to be a number that, when multiplied by

01:19

five, gives us fifteen.

01:20

If we remember anything from our multiplication tables, we know there's only one number that [Multiplication tables on a piece of paper]

01:25

does that: three.

01:26

So the rectangle has a width of three inches.

01:29

And we didn't need to put up a single missing poster.

01:31

Thanks, math, for saving us all that tape! [Man sticking missing poster on lamp posts]

01:34

We can use a similar process with perimeters.

01:37

Take a look at this rectangle.

01:38

We know that two sides are each six inches long, and that it has a total perimeter of

01:42

20 inches, but what are the lengths of the remaining sides? [Rectangle with missing lengths]

01:46

Let's take a look at our formula for perimeter.

01:49

It's what we get when we add up the lengths of all the sides. [Formula for perimeter beside a rectangle]

01:52

We know that the perimeter is twenty inches…

01:54

…and two of the sides are six inches long.

01:57

Plus, since the other two sides are opposite sides of a rectangle, they're the same length.

02:02

But what is that length? [Question mark inside a rectangle]

02:04

We could try five inches.

02:05

Unfortunately, when we add those lengths up, we get 22 inches, not 20.

02:09

And unless there are some big changes in Mathland, 22 is definitely not equal to 20.

02:14

Let's try something slightly smaller, like four inches.

02:17

And…..bingo!

02:18

We're in luck!

02:19

This math actually works out, so the remaining sides are each four inches long. [Rectangle displaying the number 4 for the missing lengths]

02:23

Now…could someone help us find our retainer?

02:26

We're thinking it might be in the crème brulee….[Retainer lodged in the middle of a creme brulee]