Surface Area of a Rectangular Pyramid | Math with Mr. J - Free Educational videos for Students in K-12

Surface Area of a Rectangular Pyramid | Math with Mr. J - By Math with Mr. J

Transcript


00:0-1	Welcome to Math with MR . J . In this
00:04	video , I'm going to cover how to find the
00:06	surface area of a rectangular pyramid . And remember surface
00:11	area is the total area of the outside or surface
00:14	of a three dimensional shape . When it comes to
00:18	rectangular pyramids , we have five total faces , The
00:22	base and four lateral faces . The lateral faces are
00:26	the triangular faces going around the pyramid , so to
00:29	speak . We need to find the area of all
00:32	of these and then add them together to get the
00:35	total surface area . So let's jump into our example
00:39	. And start by writing out surface area equals the
00:45	area of the base plus the lateral area . Then
00:51	we need to plug in our information so we need
00:54	to calculate the area of the base and all of
00:57	the lateral faces . Then add them together . Let's
01:01	use the net on the right side of the screen
01:04	to help us do this . You can think of
01:06	a net as an unfolded three D . Shape .
01:09	It shows us all of the parts , so to
01:11	speak . Let's start with the area of the base
01:15	. So we have a rectangular base so we can
01:18	use the formula area equals length times . With Now
01:23	I'm going to use the bottom portion of the screen
01:26	to show all my work as far as where I'm
01:29	going to calculate the areas . So let's come to
01:32	the bottom left area equals length times . With .
01:38	Now we plug in so our base has a length
01:43	of nine m and a width of five m .
01:48	So nine times five . Now , if you use
01:53	five for the length and nine for the with that
01:56	would work as well . Don't get too held up
01:58	on which one is length or with , because nine
02:01	times five is the same as five times nine .
02:04	Both will give you the correct area . So the
02:08	area of our rectangular base is 45 square meters .
02:16	I'm going to put a capital B above that .
02:19	So we know that that is the area of the
02:21	base . Now that we have the area of the
02:24	base , we can move to the lateral faces .
02:27	And since we do not have a regular base ,
02:31	regular means all of the sides are the same and
02:34	this is not the case . This means that we
02:36	will have two different slant heights and therefore to different
02:40	areas for our lateral faces . These will have the
02:44	same area , the top and bottom of the net
02:48	because they have the same base nine m and same
02:51	height eight and 38/100 metres . The left and right
02:58	. We'll have the same area because they have the
03:01	same base of five m and same height of nine
03:05	and 18/100 metres . So let's calculate the top and
03:10	bottom lateral faces of the net . First these would
03:13	be the front and back lateral faces of the three
03:17	D . Shape on the left hand side of the
03:19	screen . Now since we're working with triangles we can
03:23	use the formula area equals one half times the base
03:27	times the height . So area equals one half times
03:33	the base times the height . Now you can also
03:37	use base times height divided by two for triangles ,
03:40	multiplying by a half or dividing by two . They
03:43	will get you the same answer . So whatever formula
03:46	works best for you , that's what you can use
03:49	for finding the area of these triangles . Now we
03:52	plug in so again we're going to do the top
03:55	and bottom from the net first so one half times
03:59	the base while these have a base of nine m
04:05	. So let's plug in nine times the height Of
04:12	8:38 . And now we're ready to calculate . So
04:18	the area of those lateral faces is going to be
04:22	37 and 71/100 . And this is square meters .
04:32	Now I'm going to label this with one star above
04:35	it . So we know that it is the top
04:38	and bottom lateral faces of that net so we can
04:42	move to the left and right lateral faces now And
04:46	we have triangles . So we will write out our
04:50	formula area equals 1/2 times base times height . And
04:55	now we plug in so 1/2 and these lateral faces
04:59	have bases of five m . So let's plug in
05:04	five And a height of nine and 1800s m .
05:10	So nine in 18 hundreds . Now we calculate ,
05:15	So that's going to give us an area of 22
05:21	And 9500 m2 . And I'm going to label this
05:29	with two stars . So we know which lateral faces
05:34	Have the area of 22 and 9500 m2 . So
05:40	once we have all of the areas calculated for our
05:44	faces , we can fill in our net to show
05:47	exactly which areas go where and it will help us
05:51	stay organized . So we know that the area of
05:54	the base was 45 m2 . So let's Plug that
06:01	in there . And then our one star lateral faces
06:07	. 37 and 71:00 m2 . So let's label those
06:17	. And I'll put this one on the outside here
06:21	. So 37 and 71,000 m2 . And this goes
06:26	right here . And now we have the two star
06:30	lateral faces , the left and the right . 22
06:34	and 9500s . So let's squeeze this in here .
06:38	22 In 9500s m2 . And then 22 In 9500s
06:48	m2 . Goes right here . So we again have
06:53	the areas for all of our faces , the base
06:57	and then the lateral faces . So now it's time
07:01	to add everything up to calculate that total surface area
07:05	. Now let's come back up top and add these
07:08	. So we have surface area equals the area of
07:12	the base 45 Plus . Now we have all of
07:17	our lateral faces . Let's start with the top and
07:20	bottom . So 37 and 71/100 plus 37 71/100 .
07:28	Now , I'm going to have to go below here
07:30	in order to squeeze everything in . And now we
07:32	have the left and right . So 22 in 95/100
07:37	plus 22 95/100 . So you can see that we
07:42	added five numbers together . Five areas those represent our
07:47	five faces . Now it's time to calculate . So
07:51	the total surface area equals 166 And 32:00 m2 .
08:03	And that is our final answer . So there you
08:09	have it . There is how you find the surface
08:12	area of a rectangular pyramid . I hope that helped
08:15	. Thanks so much for watching until next time .
08:19	Peace . Yeah , yeah , yeah .

Summarizer

DESCRIPTION:

OVERVIEW:

Surface Area of a Rectangular Pyramid | Math with Mr. J is a free educational video by Math with Mr. J.

This page not only allows students and teachers view Surface Area of a Rectangular Pyramid | Math with Mr. J videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.