WEBVTT
00:00:00.800 --> 00:00:06.920
Find the lateral area of the given prism to the nearest square centimeter.
00:00:07.920 --> 00:00:14.680
Lateral area is the surface area of the sides excluding the top and bottom.
00:00:15.280 --> 00:00:23.880
So here it’s not the top and bottom because the bottom actually isn’t the base.
00:00:24.280 --> 00:00:27.280
It’s not laying on the bottom.
00:00:27.680 --> 00:00:29.560
This is a triangular prism.
00:00:30.280 --> 00:00:35.000
A prism is made up of rectangles and its two bases.
00:00:35.600 --> 00:00:39.440
And the bases are what distinguish what kind of prism it is.
00:00:40.280 --> 00:00:43.960
So here we have the triangles as our bases.
00:00:44.600 --> 00:00:46.760
So it becomes a triangular prism.
00:00:47.280 --> 00:00:58.160
So the lateral area will be the area of the sides excluding the top and bottom, which are the bases, the triangles.
00:00:59.280 --> 00:01:12.800
So the area that we need to find will be this rectangle, which is a 10 by 16, because we know this length is 16.
00:01:13.520 --> 00:01:16.840
We also need to find the area of this rectangle.
00:01:17.440 --> 00:01:24.280
And that’s a 16 by — we actually don’t know that length.
00:01:24.680 --> 00:01:31.760
But we do know we have a right triangle with sides 10 and 15.
00:01:32.600 --> 00:01:38.400
So we can use the Pythagorean theorem to find it.
00:01:39.120 --> 00:01:41.840
10 and 15 would be the legs.
00:01:42.400 --> 00:01:57.120
And we can call the hypotenuse 𝑥, because the Pythagorean theorem states the square of the longest side, the one across from the 90-degree angle, is equal to the sum of the squares of the shorter sides, the 10 and 15.
00:01:57.800 --> 00:02:04.680
So 100 plus 225 is 325.
00:02:05.920 --> 00:02:14.640
And now we need to square-root both sides, which is about 18.03.
00:02:15.400 --> 00:02:20.160
So we can go ahead and label that on our diagram.
00:02:20.840 --> 00:02:28.000
So here we’ve recognized the two rectangles we need to find the area for to find our lateral area.
00:02:28.520 --> 00:02:33.080
There’s one more rectangle, the one on the bottom.
00:02:33.640 --> 00:02:36.600
And it’s 15 by 16.
00:02:37.520 --> 00:02:41.040
So let’s write out all of the areas that we need to find.
00:02:42.000 --> 00:02:45.560
The first rectangle was 10 by 16.
00:02:46.400 --> 00:02:53.480
And we find the area of a rectangle by length times width, so 10 times 16.
00:02:54.200 --> 00:03:00.640
Our next rectangle is 16 by 18.03.
00:03:01.560 --> 00:03:03.520
So we’ll multiply those.
00:03:03.920 --> 00:03:09.200
And lastly, we have a 15-by-16 rectangle.
00:03:09.760 --> 00:03:12.760
So we need to multiply and then add these together.
00:03:13.080 --> 00:03:28.840
So we have 160 plus 288.48 plus 240, which gives us 688.48.
00:03:29.440 --> 00:03:33.560
However, it says to round to the nearest square centimeter.
00:03:33.560 --> 00:03:34.480
So we look here at the four.
00:03:35.200 --> 00:03:49.560
Since the four is less than five, it will keep this eight an eight, resulting in 688 centimeters squared because this is an area.
00:03:50.240 --> 00:03:53.160
So it should be square centimeters.
00:03:54.160 --> 00:03:57.320
Now there’s also another way to do this problem.
00:03:57.880 --> 00:04:05.120
We could have used the formula for lateral area, which is the perimeter of the base times the height of the prism itself.
00:04:05.960 --> 00:04:08.800
So the bases were the triangles.
00:04:09.360 --> 00:04:13.240
So in order to find the perimeter, we need to add up all of the sides.
00:04:13.960 --> 00:04:24.440
So we have 10 plus 15 plus 18.03, giving us 43.03.
00:04:25.320 --> 00:04:30.600
Now the height, the height of a prism is the distance between the bases.
00:04:31.200 --> 00:04:34.720
So here’s our other triangle, the other base.
00:04:35.480 --> 00:04:40.560
So the distance between these two triangles would be 16.
00:04:41.200 --> 00:04:57.040
So we have 43.03 times 16, which gives us 688.48, which is exactly what we got before.
00:04:57.600 --> 00:05:04.360
So we would have rounded to be 688 square centimeters.
00:05:05.000 --> 00:05:07.000
So either way will work.
00:05:07.400 --> 00:05:14.320
And we would still result in the same answer, 688 square centimeters.