Hi! Welcome to Math Antics. In this lesson, we’re going to learn about an important concept in Geometry called Perimeter. “Perimeter” is just a fancy math term that means the distance (or length) around a shape. …but
what exactly does the distance around a shape mean? Well… distance (or length) is a 1-dimensional quantity that we can measure with units like
centimeters, inches or miles. That means that perimeter is also a 1-dimensional quantity that we can measure with units of length. For example, the perimeter of a shape wouldn’t be just 10, but it could be 10 cm. Or, instead of being just 25, it could be 25 miles. The units are REALLY important
when you’re talking about perimeter! Okay, but what exactly do we mean by,
“around a shape”? It seems like there would be a lot of different ways
to go around a shape. Some of them would be short
and some of them would be very long. Well, perimeter means the absolute shortest distance possible around a shape. That would be the distance you’d get if you traced the path exactly around the border (or edge) of a shape. A good way to see what perimeter is, is to imagine that you could walk right along the edge of a shape, like this 5-sided polygon. Imagine starting at one of the polygon’s vertices and then walking along each side until you got all the way back to the point that you started from. The total distance you traveled would be the perimeter of that shape. In this case, if the length of each side of the polygon was 10 meters, the total length you would travel along all 5 sides would add up to 50 meters. Another good way to see what perimeter is, is to imagine that you could take a shape, like this square, and break it at one of its corners. Then, you could unfold the shape until it formed a straight line. The length of that line is the perimeter of the shape. Doing this helps you understand why perimeter is a 1-dimensional quantity, even though it applies to 2-dimensional shapes like this square. It’s 1-dimensional because its the distance of the lines that go around the 2-dimensional shape. Okay, so now that you know what perimeter is, how do we measure or calculate it for different geometric shapes? Well… that depends on the shapes. Finding the perimeter of shapes that have curves, like circles or hearts or things like that, can be tricky. In fact, we’ll wait and talk about the perimeter of a circle in another video. In this video, we’re just going to focus on how to find the perimeter of polygons. Since polygons are made from only straight sides, it’s easy to find their perimeter. If you know the length of each side, all you have to do is add them up, and the total length you end up with is the perimeter of the polygon. Let’s try doing that with a few examples so you see how it works… the first polygon we’ll try is a triangle. This triangle has three sides that are each a different length: 3cm, 4cm and 5cm. Now, to find the perimeter of the triangle, all we have to do is add up the lengths of those three sides. 3 + 4 + 5=12 But… don’t forget. It’s not just 12. It’s 12 centimeters. Always remember to also put down the units of the perimeter. Okay, that was easy. Let’s try another one. This time our polygon is a rectangle. And you can see that the shorter sides are each 5m long and the longer sides are each 10m long. So… let’s add them all up. We can add up the sides in any order we want to, as long as we don’t forget any sides or accidentally count any of them twice. And I think I’ll add up the two short sides first. 5 + 5=10 Next, I’ll add up the two longer sides. 10 + 10=20 And now, if I add up those two answers, I’ll get the total for all 4 sides. 10 + 20=30 So, the perimeter of this rectangle is 30… …METERS! Ha! You thought I was going to forget my units, didn’t you. Not this time! Ah, here’s another good example. This is a 6-sided regular polygon. A ‘regular’ polygon means that all its sides are exactly the same length. That’s good because this diagram only shows the length of ONE side. (4 cm). But since the polygon is regular, we know that all the sides must also be 4 cm long. Now, we could just add up all the sides like we did before, but since they are all the same, we can use multiplication as a shortcut. That’s because multiplication is really just repeated addition. All we have to do is multiply the number of sides (6) by the length of the sides (4 cm). 6 x 4=24 so that means the total perimeter must be 24. 24 what? . Ooo – Centimeters !!! That’s better. . [oops] And this formula works for ANY regular polygon, no matter how many sides there are. If the sides are ALL THE SAME LENGTH, you can just multiply the number of sides by the side length, and you have the perimeter! Okay, let’s try one more example. This polygon also has six sides but it’s NOT a regular polygon. The sides are different lengths and this one’s really tricky because they only show us
the length of four of the sides. The other two are missing!
So how can we figure them out? Problems like this come up all the time in math; problems where you aren’t quite given all the information. When you have this kind of problem, the key is to use what you DO know to figure out what you DON’T know. Here’s what I mean… Look closely at the two vertical sides that we DO know the lengths of (4 inches and 6 inches) Now… imagine that those two vertical sides could be moved straight across to the other side… the side that we don’t know the length of. By doing that, you can see that the missing length would just be the combination of the two vertical lengths we DO know: 4 inches and 6 inches. And since 4 + 6=10, the missing vertical side must be 10 inches long. Notice that we can do the same thing for the horizontal sides that we do know. If we imagine those moving down to the side that we don’t know, we see that it’s length must equal the combination of those two lengths. 10 inches plus 5 inches equals 15 inches. There, we’ve used the lengths that we DID know to figure out the lengths that we DIDN’T know. And now that we know the length of ALL the sides, we can just add them all up to get the perimeter. 4 + 5 + 6=15 And then 15 + 15=30 30 + 10=40 and last of all, 40 + 10=50 So, the sum of all the sides is 50 inches.
That’s the perimeter of this shape. And that’s the end of this lesson. We’ve learned that Perimeter is the distance (or length) around a geometric shape, and we’ve learned how to calculate it for any polygon. You just add up the lengths of all the sides and the total length is the perimeter. Oh… and don’t forget your units! Also, don’t forget that to get good at math takes practice! Thanks for watching Math Antics
and I’ll see ya next time. Learn more at www.mathantics.com