Finding perimeter when a side length is missing | Math | 3rd grade | Khan Academy

What is the perimeter of the figure below?

So down here we have this figure and we are asked to find the perimeter of this figure. Perimeter is the distance all the way around the outside of a shape.

So in this case, if I were to walk around the outside, or maybe a human's too big if an awesome little ant was to walk all the way around the outside of this figure, how far she walked would be the perimeter.

To find that, what we can do is figure out how long this side is and then combine it with the length of this side, and combine it with the length of this side. Once we combine all of the side lengths, we'll have the perimeter or the distance around the outside of the figure.

So let's start. We can start up here; we can see that this side length is 5 centimeters.

So we have five centimeters plus moving down the side here we have another three centimeters. Then going across, the next distance is four centimeters. After that we go down this side right here which is another four centimeters.

As we keep going across the bottom, we have another nine centimeters, and then we head up this side and, uh oh, we don't have a label. We don't know how far this is, but to find perimeter we need the distance around the entire outside.

If this little ant, she walked the whole way, we've got to know the entire distance she walked. So what we can do is we can look over here and say this length right here is 3 centimeters. Well, then that same length over here is also three centimeters.

Where that three centimeters left off, this four centimeters, this length picked up. So from here to here is another four centimeters.

So if we have four centimeters plus another three centimeters, that's a total of seven more centimeters.

So now we know all of the lengths around the outside. If we combine them or add them, we'll know the perimeter.

So we can start: five plus three is eight, four plus four is another eight, nine plus seven, let’s see, instead of seven I could do nine plus one and six because that's the same as seven.

Nine plus one is ten, and ten plus six is sixteen. Eight plus eight is another sixteen, so we have a sixteen and a sixteen.

Let’s see, six ones plus six more ones is twelve ones and one hundred plus another hundred, or one hundred plus one hundred is two hundred.

So another way we could add this is twenty plus twelve, which is a total of thirty-two.

And we were talking about centimeters here, so thirty-two centimeters. The distance all the way around the outside of this figure, or the perimeter of the figure, is thirty-two centimeters.