WEBVTT
00:00:00.920 --> 00:00:03.760
Work out the surface area of the prism.
00:00:05.080 --> 00:00:09.280
The diagram shows a prism whose cross section is a trapezium or trapezoid.
00:00:09.840 --> 00:00:18.000
In order to find the surface area of this prism, we need to find the areas of each of its faces and then add them together.
00:00:18.800 --> 00:00:26.520
This prism has six faces of various different shapes, so we’ll calculate each of their areas.
00:00:27.160 --> 00:00:34.120
Let’s begin with the only two faces that are the same, the front and the back of the prism.
00:00:34.640 --> 00:00:37.480
These two faces are each trapeziums.
00:00:38.000 --> 00:00:45.320
We can see this because the blue arrows indicate that two of the sides are parallel.
00:00:46.120 --> 00:00:56.040
To find the area of a trapezium, we find the average of the two parallel sides and then multiply by the perpendicular distance between them.
00:00:56.760 --> 00:01:02.960
This gives a calculation of six plus nine divided by two and then multiplied by four.
00:01:03.440 --> 00:01:09.160
Remember, there are two of these faces, the front and the back of the prism.
00:01:09.880 --> 00:01:14.160
So we’ll also multiply by two in order to find both areas.
00:01:14.680 --> 00:01:22.160
This gives a contribution of 60 to the total surface area from the front and the back.
00:01:23.240 --> 00:01:27.040
Next, let’s think about the top of this prism.
00:01:27.720 --> 00:01:33.800
The top of the prism is in fact a square with sides of length six units.
00:01:34.440 --> 00:01:39.560
Therefore, its area is calculated by multiplying six by six.
00:01:40.240 --> 00:01:48.920
This gives a contribution of 36 to the total area from the top of the prism.
00:01:49.520 --> 00:01:54.000
Next, let’s consider the area of the sloping face of the prism.
00:01:54.560 --> 00:02:01.280
This sloping face is a rectangle with sides of length six and five units.
00:02:01.800 --> 00:02:13.800
Therefore, its area is found by multiplying six by five, and so we have a contribution of 30 from the sloping face of the prism.
00:02:14.480 --> 00:02:19.720
Now, there are two more faces of this prism that aren’t actually visible on the diagram.
00:02:20.360 --> 00:02:22.240
The first of these is the base.
00:02:22.880 --> 00:02:30.160
The base of the prism is another rectangle, this time with sides of length six and nine units.
00:02:30.680 --> 00:02:42.880
Therefore, its area is found by multiplying six by nine giving a contribution of 54 to the total surface area.
00:02:43.960 --> 00:02:48.280
The final of the prism’s six faces is the vertical face.
00:02:48.760 --> 00:02:53.840
This is also a rectangle and its dimensions are six units and four units.
00:02:54.480 --> 00:02:59.360
It is this measurement of six units here that we’re using.
00:02:59.960 --> 00:03:10.400
So to find the area, we multiply six by four giving a contribution of 24 to the total surface area.
00:03:11.080 --> 00:03:15.440
So we have the areas of each of the individual faces worked out.
00:03:15.800 --> 00:03:21.960
And to find the total surface area, we now just need to sum all of these areas together.
00:03:22.680 --> 00:03:33.800
So we have 60 plus 36 plus 30 plus 54 plus 24.
00:03:34.240 --> 00:03:39.080
Remember that 60 represents two of the faces of the prism.
00:03:39.600 --> 00:03:44.400
And we have a total of 204 for the surface area.
00:03:44.840 --> 00:03:52.040
Now we haven’t been given any units in the diagram, so this is just general area units.