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  • Hi! Welcome to Math Antics.

  • In this lesson, were going to learn about an important concept in Geometry called Perimeter.

  • Perimeteris 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 youre 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, well wait and talk about the perimeter of a circle in another video.

  • In this video, were 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 well 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

  • Butdon’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 ‘regularpolygon 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, weve 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.

  • Weve learned that Perimeter is the distance (or length) around a geometric shape,

  • and weve 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

Hi! Welcome to Math Antics.

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Math Antics - 周長 (Math Antics - Perimeter)

  • 1725 9
    Yassion Liu 發佈於 2021 年 01 月 14 日
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