WEBVTT
00:00:02.110 --> 00:00:05.140
Let’s talk about finding the area of a triangle.
00:00:06.040 --> 00:00:13.620
And I guess before we talk about finding the area of a triangle we need to talk about what the area is.
00:00:14.210 --> 00:00:19.550
Area is really simply a size of a surface.
00:00:19.900 --> 00:00:28.850
So here you can see I just coloured in the surface of this triangle, and we want to figure out how big it is.
00:00:29.260 --> 00:00:30.240
So let’s dive in.
00:00:33.090 --> 00:00:36.990
Okay, I know what you’re thinking, “These aren’t triangles!”
00:00:37.480 --> 00:00:49.650
But before we figure out how to find the area of triangles, I want us to take a step back and try and remember how do we find the area of a parallelogram.
00:00:49.680 --> 00:00:57.720
So we can find the area of a parallelogram here, a square here, or a rectangle.
00:00:57.900 --> 00:01:08.350
But, if you remember, when we find the area of a rectangle, we take the length and we multiply it by the width.
00:01:08.490 --> 00:01:16.050
Another way to write that, sometimes we say the base and we multiply it by the height.
00:01:16.470 --> 00:01:20.720
Either way, we got length and width, base and height, doesn’t matter.
00:01:21.080 --> 00:01:28.910
We take these two numbers and we multiply the base times the height to find the area.
00:01:29.570 --> 00:01:36.370
But now what I want us to do is I want us to cut these guys in half, okay?
00:01:36.900 --> 00:01:42.660
We’re gonna cut our parallelograms, our quadrilaterals, in half.
00:01:43.110 --> 00:01:55.110
And what you should start to see is that every one of these is made up of two triangles, two equal triangles.
00:01:55.680 --> 00:01:56.630
How does this matter?
00:01:56.630 --> 00:01:57.850
Why does this matter?
00:01:58.020 --> 00:01:59.100
We’re gonna find out.
00:02:01.420 --> 00:02:07.510
So remember, we said the area of this square would be base times the height.
00:02:08.110 --> 00:02:13.480
But our goal here is to find out the area of a triangle.
00:02:14.290 --> 00:02:36.290
Well the thing is this triangle is half of the square, so the formula for finding the area of a triangle is by taking half of what the quadrilateral’s area would be: base times height divided by two is the simple way we say it.
00:02:36.320 --> 00:02:40.100
So we say base times height and divide it by two.
00:02:40.860 --> 00:02:41.550
Let’s try it.
00:02:43.250 --> 00:02:45.130
Okay, here’s our first example.
00:02:45.560 --> 00:02:52.550
So someone has already told us the base and the height, the height and the base of this triangle.
00:02:52.890 --> 00:03:02.760
So what we need to start with then is our formula, which we remember is area equals the base times the height divided by two.
00:03:03.440 --> 00:03:11.850
All we need to do is figure out that the base is eight and the height is four.
00:03:12.040 --> 00:03:20.410
We can plug that into our formula by saying eight times four divided by two, okay?
00:03:21.110 --> 00:03:23.400
Eight times four divided by two.
00:03:24.630 --> 00:03:36.730
Eight times four is thirty-two, and then we divide thirty-two by two for a final answer of sixteen.
00:03:38.030 --> 00:03:43.990
So before we move on, I wanna tell you something really important about the area.
00:03:44.500 --> 00:03:52.740
Our answer is not just sixteen; our answer is sixteen centimeters squared.
00:03:53.380 --> 00:04:01.350
Any time we’re dealing with area, it’s so important that you know what it is that you’re working with.
00:04:01.350 --> 00:04:03.780
What are we measuring our triangle in?
00:04:04.120 --> 00:04:12.980
And this time, we’re measuring our triangle in centimeters, so we wanna make sure that we include our centimeters squared.
00:04:14.660 --> 00:04:24.000
Okay example two, this time again we’ve been given all of our measurements: we’ve been given three, four, and five.
00:04:24.760 --> 00:04:34.610
So what I want you to be careful of when you’re trying to solve the area of triangles is knowing what is the height and what is the ba-what is the base.
00:04:34.610 --> 00:04:38.490
So here is the key to finding the height and the base.
00:04:39.030 --> 00:04:43.220
You first need to look for the right angle, okay?
00:04:43.580 --> 00:04:49.360
So your height and your base will always be connected to the right angle portion.
00:04:50.150 --> 00:04:55.770
So if we go back to our last example problem, it looked like this, right?
00:04:56.250 --> 00:04:59.300
But remember, we had this symbol.
00:04:59.760 --> 00:05:05.390
We had a little symbol right here that told us, “Oh! height and base.”
00:05:05.560 --> 00:05:08.170
When we’re dealing with a right triangle, it’s the same.
00:05:08.730 --> 00:05:14.210
We have this right angle which tells us, “Okay here’s our base, and here’s our height.”
00:05:14.420 --> 00:05:19.760
And the thing is, right now we do not even need this five meters.
00:05:20.530 --> 00:05:37.670
We don’t need that five meters to figure out anything about the area, so we can ignore that guy and we can move on and say three meters times four meters divided by two is gonna give us the area of this triangle.
00:05:38.250 --> 00:05:42.340
So we say three times four is twelve, divided by two.
00:05:43.110 --> 00:05:48.840
And again, that’s six but we do not forget these meters.
00:05:49.360 --> 00:05:52.540
We bring our meters down, and it’s meters squared.
00:05:52.910 --> 00:05:56.370
We deal with area; we deal with our units, squared.
00:05:58.310 --> 00:06:00.420
Example three is for you.
00:06:00.930 --> 00:06:05.030
So what I want to do to you right now is just stop what you’re doing, pause.
00:06:05.780 --> 00:06:10.900
Pause the video, and write this down and see if you can find the area of this triangle.
00:06:11.160 --> 00:06:12.660
Go ahead pause it; I’ll wait.
00:06:15.180 --> 00:06:17.760
The answer is thirty feet squared.
00:06:17.990 --> 00:06:20.440
So I hope you got that and you were successful.
00:06:20.440 --> 00:06:25.440
But if you didn’t get the whole problem, then don’t worry I’m gonna walk you through this one again.
00:06:26.010 --> 00:06:34.410
So area, first we write our formula area equals one-half times the height times the base.
00:06:35.500 --> 00:06:43.210
We figure out that the right angle tells us which one is the height and which one is the base.
00:06:43.670 --> 00:06:48.880
So we have a ten-foot base, and we have a six-foot height.
00:06:49.560 --> 00:06:51.670
You need to divide that by two.
00:06:52.210 --> 00:06:56.350
Six times ten is sixty, divided by two is thirty.
00:06:56.700 --> 00:07:05.590
And again, we say this is area; we can’t forget our units, thirty feet squared.
00:07:07.510 --> 00:07:12.760
Now you’re ready to go out and solve all the triangle area problems.
00:07:13.030 --> 00:07:27.950
Just remember these two key things: one, that your formula is area equals height times the base divided by two and, number two, always add the unit squared at the end.
00:07:28.270 --> 00:07:29.290
You’ll be good to go.
00:07:29.940 --> 00:07:31.650
Happy area finding!