Up next in 10
PERIMETER AND AREA: How To Solve problems involving rectangles and triangles
57 views
Feb 19, 2025
We've already learned how to find values of algebraic expressions by substituting values for variables. We've also learned how to solve two steps equations. In chapter 5.1, we'll learn how to solve problems involving the perimeters of triangles and rectangles. We'll also learn how to solve problems involving the areas of triangles and rectangles. Some of the new vocabulary we're going to be introduced to are formula, perimeter and area. Chapters: 00:00 Introduction 03:24 Perimeter of a rectangle 04:14 How to find the perimeter of a triangle 07:18 How to solve for a missing side 11:30 How to find the area of rectangle 12:36 How to find the area of a triangle
View Video Transcript
0:00
[Music]
0:00
all right so we're talking we're done
0:02
with chapter 4 right we got our chapter
0:05
four um text that's done with chapter
0:07
four so now we talking chapter 5 one
0:10
okay it's just easier than chapter
0:12
chapter 5 is pretty much it's not I can
0:14
say it's easier but more
0:18
like much better right but it's still
0:21
the same principle we still going to be
0:22
doing equations and stuff like that
0:24
right right so
0:26
now we are talking perimeter and areas
0:31
and then why are we doing this is it
0:33
important yes right because you talking
0:36
about perimeters you talk about areas
0:38
constantly areas like the surface right
0:41
perimeter is what the outline or the
0:43
Contour right okay so example if you
0:47
want to rent a place you want to you ask
0:49
usually people ask how much is a square
0:51
footage right how big is the house 3,000
0:54
ft you that's that's area right area is
0:57
expressed in terms of what Cu uh square
0:59
m
1:00
Square in square whatever the thing is
1:02
square feet now perimeter is usually uh
1:06
the distance around a geometric figure
1:09
right now what is the formula before we
1:11
do that a formula is an equation that
1:14
shows the relationship among certain
1:17
quantities right I want to find the
1:18
formula you know eal mc² that's the what
1:22
the formula for what relativity Einstein
1:25
came up with that right so the formula
1:27
pretty much tells you the relationship
1:29
between
1:30
like certain quantities like for example
1:32
we have the formula to find uh the
1:37
perimeter of a rectangle right the area
1:39
to the the formula to find the perimeter
1:42
of a triangle all of those things are
1:44
stuff that people have established and
1:46
now we can use them to solve a problem
1:49
okay now the first one we're going to
1:51
talk about is perimeter and then we're
1:52
going to get to areas so if I want to
1:54
ask you to find the perimeter of this
1:57
room so what would you do how would you
1:59
find the perimeter this one yes um I
2:02
would measure each side or I would
2:04
assume that it's like rectang a perfect
2:07
rectangle and the two sides are the same
2:10
and then I would add up the all the
2:12
sides all the side right pretty much
2:14
yeah so to find the perimeter of this
2:16
room you want to know how long is this
2:18
wall how long is that wall this wall and
2:20
behind you and then you add them all
2:22
together and that gives you the
2:23
perimeter of this entire room right do
2:26
you use it in real life yes right say
2:29
you want to put fence you have a nice
2:31
house and you want to put a big fence
2:32
around it you need to know the perimeter
2:34
because you're going to go to Home Depot
2:36
and try to find what those wooden planks
2:39
so that you can put them okay and then
2:41
set up your fence or whatever bar wire
2:43
whatever you want to put if you have
2:45
animals and you don't want Woods or
2:47
whatever to come and eat them you have
2:49
to reive wire you want to put what you
2:50
got to put that on cuz if you don't do
2:52
it wolf is going to come and chop your
2:55
stuff or fox or whatever the thing is
2:57
Right chickens so a per is very useful
3:00
we use in areas as well now to find the
3:03
perimeter of a rectangle everybody say
3:05
rectangle rectangle so in a rectangle we
3:09
have some specific dimensions right a
3:12
rectangle has what it has a length and
3:15
what what's the next measurement length
3:19
and W W width right so we have in the
3:22
rectang we have the length and we have
3:25
the width right and to find the
3:27
perimeter of a rectangle what we do we
3:30
do the sum of what the sum of twice the
3:32
length plus twice the width all right
3:36
does that make sense to find the
3:38
perimeter of a rectangle it is twice the
3:41
length plus twice the width this is
3:45
conventional when I say conventional I
3:47
mean it is uh it is a sure thing
3:50
anywhere you go in the world where going
3:53
you go to the moon to the sky to China
3:57
to whatever the perimeter is always
3:59
going to be what twice the length plus
4:01
twice the width when you have a
4:03
rectangular figure does that make sense
4:06
it does not change at all right so this
4:10
is how you find the perimeter of the
4:11
rectangle now what kind of figure is
4:13
this triangle triangle why is it
4:17
triangle three side right t r i stand
4:21
for what triangle mean three side right
4:24
three angles pretty much three sides so
4:27
to find the the perimeter of a triangle
4:29
what we we do we add all three side is
4:32
the sum of the three side like a plus b
4:36
plus C so this is how you find the
4:39
perimeter of a triangle you just add the
4:41
three sides together okay so for example
4:44
we have now this is what kind of figure
4:46
is this here rectangle rectangle how you
4:49
find the the the perimeter of this
4:52
rectangle using the formula what's the
4:55
length what's the length of this
4:57
rectangle the length is the length is 10
5:00
L is 10 what's the the width five five
5:04
right the width is five so to find the
5:06
perimeter of this rectangle we're going
5:08
to do what P right that's the letter for
5:10
the rectangle is twice the length so
5:12
that that'll be what 2 * what 10 10
5:15
right in parenthesis plus plus 2 * 5 2 *
5:18
5 right so the perimeter of this
5:20
rectangle will be 20 + 10 which is 30
5:25
right so the perimeter of this rectangle
5:27
would be 30 really easy step
5:30
right now how would you find the
5:32
perimeter of this triangle here how do
5:35
we do
5:37
it uh Dexter how do I find the perimeter
5:40
of this
5:41
triangle uh you add 8 8 7 six eight
5:47
right plus what s seven and six right so
5:53
you get 8 + 7 is 15 and 6 that's 21
5:56
what's the unit that I use here cm is
5:59
what CM cenm right so it's 21 cm okay 21
6:03
cm now in a problem if they give you the
6:06
unit make sure you keep that right you
6:09
do not just write 21 21 will be false we
6:11
are talking about measurement so it has
6:13
to be 21 cm so you have to make sure you
6:16
respect the unit yeah when you're
6:18
solving it like um 8 cm+ 7 cm plus 6 cm
6:23
is it okay to just use um 8 + 7 + 6 and
6:27
make sure in your um
6:30
your answer to parentheses uh no the it
6:35
doesn't matter um you put centimeter at
6:38
the end right
6:40
yeah so just like writing centimeter on
6:43
the answer like on the actual problem
6:46
yeah you can do it like this you can
6:47
have 8 + 7 + 6 parenthesis
6:51
CM right that means everything is in
6:54
centimeter and then you add them up and
6:55
you get 21 cm that would be right as
6:58
well okay I don't put cenim in the if
7:02
it's just 8 + 7 + 6 = 21 cm yeah that's
7:06
fine I just want to make sure at the end
7:07
you give me the unit is 21 cm okay now
7:11
now we're going to work on the word
7:12
problem okay all look right so now I
7:16
want you to think here we use our head
7:19
right the perimeter of a rectangle is 42
7:22
ft right they're giv us a perimeter
7:24
they're telling us the perimeter is 42
7:26
ft and now it's they want us to find its
7:29
length if it's with Excuse me it's 10 ft
7:33
so how do we solve this
7:35
problem think about it for a second we
7:38
have the the the perimeter is
7:41
given the length is not given the width
7:44
is given so how do we find the length
7:46
yeah um I would I'm a visual learner so
7:50
I would draw a rectangle good so visual
7:53
learner we draw a rectangle that's
7:54
excellent I would put the width as 10
7:56
the width is he on the top or the bottom
7:59
or the sides side right this is 10 so
8:02
that mean this is also what the other
8:05
side is 10 this is also 10 right write
8:08
um like P equal 42 all right do we know
8:11
l no so what do we put there question
8:14
mark or X if you want we can put X or
8:17
question mark right now we know that P
8:19
is what 42 42 ft now what do we know
8:24
about the formula here that we know that
8:27
um 10 + 10 20 plus something = 42
8:31
excellent
8:32
42 right but we got to go step by step
8:35
cuz we not trying to rush it right we
8:36
know that P right is equal to what 2 L +
8:40
2 what w right do we know
8:44
P yes what is
8:47
p 42 what so we can set it up as an
8:50
equation yeah set it up as an equation
8:52
that's the right word 42 ft = to 2 L
8:56
right plus 2 * what what's w 10 10 10 ft
9:01
right there you go you see what we doing
9:03
here now we set up an equation does that
9:06
make sense to everybody right so now we
9:08
have an equation and now we can solve
9:10
this equation for what L because that's
9:13
what we looking for right so now this is
9:16
42 because we don't want to deal with
9:18
the feet right now we just going to
9:19
leave it as 42 = 2 L what's 2 * 10 20 20
9:24
right now how do I solve for two for L
9:27
here first you have to do what subra 20
9:30
you remember so that's from chapter what
9:32
chapter 4 you see that everything is
9:34
building up to this right now we have to
9:36
solve so now this is assuming that you
9:38
already know these things right so we
9:39
have to stop subtract 20 right so we got
9:43
22 = to 2 L and then how do you find L
9:47
divide by two divide by two there you go
9:50
L = 11 L = 11
9:54
what now what's the unit here Fe so L is
9:58
equal to 11 ft so therefore the length
10:02
of this rectangle is 11 ft is it
10:04
confusing to anybody
10:09
here f is
10:12
it yeah this left yeah what does that
10:14
look
10:16
like
10:19
supposedly
10:23
fine I'm have to answer your questions
10:26
multiple questions this is f is better
10:29
hey 11 ft
10:31
right right 11 ft so this is how you
10:35
find the uh length given the width or
10:39
vice versa okay so this is a word
10:41
problem okay now um now we're going to
10:45
talk about areas okay so now areas is a
10:48
little bit confusing sometimes it's not
10:51
that confusing it's just a little bit
10:52
because can I erase this all
10:57
right so now we talk perimeter now we
11:00
going to talk about area right was easy
11:02
when they gave us all the things in so
11:05
now we talk about areas and we have two
11:07
type of figures
11:15
again right
11:26
so I'm slowly trying
11:30
all right so what kind of figure is this
11:33
again rectangle how do you find the area
11:36
of a rectangle yeah um you add each side
11:41
I'm sorry multiply multiply each side
11:44
right so area is what L
11:47
* W or length time width right again the
11:52
area deals with what
11:53
surface why do we need to find an area
11:56
what is the use of it let's say you want
11:58
to put TI on
11:59
in your room right are you just going to
12:02
go to Home Depot and just buy any no you
12:05
just need to know what what is the
12:07
surface area right now once you find it
12:10
you know okay I need about 300 ft all
12:13
right this is how much I need so you
12:14
need to know the area to do that does
12:16
that make sense right if you want to put
12:18
a tire if you want to put some kind of
12:20
cloth on the table you need to know the
12:22
area this is why you use it okay all
12:26
right so now to find the area of a
12:28
rectangle we do length time width now to
12:32
find the area of a triangle that's when
12:35
it's a little bit something maybe you
12:36
have never seen before right so when you
12:39
have a rectangle ABC okay to find the
12:42
area of this rectangle this triangle I
12:44
mean you do half time base time height
12:49
half time the base time height okay the
12:51
area of a triangle is 12 base * h h h is
12:57
the height here okay you all always take
12:59
the height from the base all right so to
13:01
find the area of a triangle is half time
13:04
the base time the
13:06
height that's how you find the area of a
13:08
triangle okay half times the base times
13:11
the height does that make
13:13
sense all right so yes I have a
13:19
question um why does the half of the
13:22
base with the height work why does he
13:26
work that's that's an interesting
13:28
question may you have any investigated
13:29
that maybe I'm just like anybody else I
13:31
just memorize this for my whole life I'm
13:33
not sure why it works but somebody came
13:35
up with this this equation say hey to
13:37
find the area of a triangle is always
13:39
half times the base times the height
13:42
right like the circumference of the
13:43
circle something see yeah let me see why
13:47
half times the base times the height to
13:49
find the
13:50
area I'm not sure why maybe your mom who
13:53
know that maybe you should ask let us
13:55
like us that I just never really know
13:57
why does she work now for the rectangle
13:59
for the perimeter it works because I
14:01
know a contour but for the area I'm
14:03
trying to figure out why does that work
14:05
for the surface never thought never
14:07
thought about it that's a good question
14:09
I thought about it because I wasn't to
14:11
the equation and school
14:14
was
14:16
diagn random question and I would be
14:19
like okay I wonder how I find the area
14:21
of a triangle that's that's interesting
14:24
right anyway so you can you if you cut
14:28
this up into small
14:29
little triangles we can find the area of
14:32
each one of them the surface and that's
14:33
going to give us the area right but any
14:36
by definition to find the area of a
14:37
triangle is half * the base MTI by the
14:40
height this is how you find the area of
14:42
a triangle okay so let's say I give you
14:45
let's let's let's do a d problem here so
14:48
let's say we have this triangle here
14:50
right and we have a triangle of uh let
14:54
me look in the book may you have a good
14:56
example
14:59
so the base let's say the base here base
15:02
is 12 in right and the height is about 5
15:09
in and they want us to find the area of
15:12
this triangle now the good thing about
15:15
this problem is this to find the area of
15:16
a triangle right
15:19
uh the unit is what Ines square or feet
15:24
square is always squared whatever the
15:26
unit is right so to find the area of
15:28
this triangle here my base is 12 in this
15:31
is the bottom portion right my height is
15:33
given is 5 in now I just need to find
15:36
the area by plugging in every piece of
15:38
information in the formula so it's going
15:40
to be 12 * 5 * 6 which is a 12 which is
15:45
the base time 5 right this is how I'm
15:49
going to do it so so it's going to be 12
15:52
of 12 is 6 right so 6 is 6 * 5 and that
15:57
gives you 30 inches squared okay so this
16:02
is so 12 so it's like 12 2 * five yeah
16:07
yes yeah right so the area area is
16:11
always expressing squared whatever the
16:13
unit is okay and that should do for this
16:17
section
#Mathematics