WEBVTT
00:00:00.850 --> 00:00:03.360
Find the surface area of this triangular prism.
00:00:03.550 --> 00:00:06.650
Hint: you can draw the net of the shape to help you.
00:00:07.450 --> 00:00:09.590
So we have- that this is a triangular prism.
00:00:09.780 --> 00:00:13.170
The bases, the parallel faces, are triangles.
00:00:13.590 --> 00:00:20.700
And it’s a prism because the rest of the faces or the sides is what we can call them are rectangles.
00:00:21.120 --> 00:00:25.460
That’s what makes up a prism: the two bases and then the rest are rectangles.
00:00:25.910 --> 00:00:32.430
So if we would like the surface area of this shape, we need to add the area of all of the faces together.
00:00:33.030 --> 00:00:40.540
So our hint tells us to draw the net of this shape, which would be all of the faces laying flat so we can easily see them.
00:00:40.990 --> 00:00:42.160
So let’s go ahead and do that.
00:00:42.610 --> 00:00:51.940
So we have these two triangles, which are our bases; we have the pink rectangle, found back here; and we have this length as 15, because it matches this one.
00:00:52.440 --> 00:00:58.080
We have the bottom rectangle, and keep in mind that these are not to scale, and then lastly the blue rectangle.
00:00:58.440 --> 00:01:00.410
So here we’ve drawn the net of the shape.
00:01:00.730 --> 00:01:06.540
So if we find the area of each of these shapes and we add them together, we will have the surface area.
00:01:07.040 --> 00:01:10.250
The area of a triangle is one-half times the base times the height.
00:01:10.800 --> 00:01:17.840
So for the two rectangles, we have one-half times their base of eight times their perpendicular height, which is six.
00:01:18.100 --> 00:01:25.700
And it’s important that we know that that’s a right angle in the corner of the triangle, because that let’s us know that the six is indeed perpendicular.
00:01:26.470 --> 00:01:27.890
So we won’t be using the 10.
00:01:28.440 --> 00:01:32.960
So we can either take that and multiply by two or write it twice since we have two triangles.
00:01:33.530 --> 00:01:37.060
Now we have the rectangles, and the area of a rectangle is length times width.
00:01:37.520 --> 00:01:47.140
So we need to take six times 15 for the pink rectangle, eight times 15 for the green rectangle, and 10 times 15 for the blue rectangle.
00:01:47.500 --> 00:01:48.750
So let’s begin to simplify.
00:01:49.100 --> 00:01:55.670
One-half times eight times six, well one-half times eight is four, and four times six is 24.
00:01:55.970 --> 00:01:58.720
So we’ll repeat that process again for the second triangle.
00:01:59.140 --> 00:02:09.550
And then we have six times 15, which is 90, and then eight times 15, which is 120, and then 10 times 15, which is 150.
00:02:09.910 --> 00:02:12.260
Adding these numbers together, we get 408.
00:02:12.830 --> 00:02:23.190
Now we don’t have any units for this shape, so we could say that it’s an area of 408 square units because an area should be squared.
00:02:23.720 --> 00:02:25.220
And this will be our final answer.