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welcome to math with mr j
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in this video i'm going to cover how to
find the surface area of a rectangular
prism
and remember when it comes to surface
area simply put
it's the total area of the outside part
or
layer of a 3d figure so when it comes to
rectangular prisms
they have six faces so we need to find
the area
of each face and add all of that up in
order to get the surface area
now at the top of your screen in blue we
are going to use
that formula there in order to find
the surface area of a rectangular prism
so surface area
equals 2 times front or back plus
2 times right or left plus 2
times top or bottom so let's talk about
what that means
now i have everything multiplied by 2
because for example if we pick the front
or back let's say we pick the front here
if we find the area of the front
we can multiply that by two because the
back
is the exact same as the front same with
right and left we can find the area of
the right face
and then multiply it by 2 because the
left
is the exact same as the right
same with top and bottom so let's get
into finding the surface area here
and we'll start with surface area
equals 2 and we need to find the
area of the front or back so let's find
the area of the front where we have a
6 by
two so we can do area
equals length times width for a
rectangle plug in
area equals six times a width
of two and we get an area
of 12 square inches
for the front so we could plug in 12
here plus now we need to do the right
and left now but before i get to that i
want to mention
to the right here i have a net of that
rectangular prism so basically i
unfolded it
so you can see all of the faces
and it's not in 3d form so it kind of
lays everything out so we can visualize
what we're doing a little better
so as of right now we have 12 square
inches here for the area of the front
and the back
so let's do right and left so we'll pick
the right side here the right face
and we have a three by two
so area equals length times width so we
can plug in
three times two and that gives us an
area of
let's actually write it out length times
width
area equals 3 times 2 so that area is
going to be
6 square inches so again that's the
right
and left
so we would do 2 times 6
for the right and left and lastly we
need to do the top
and the bottom so we're going to take a
look at the top
where we have a six by three
so area equals length times
width plug in six
times three and we get an area
of 18 square inches so our bottom
is 18 square inches and our top is 18
square inches so we would plug in 2
times 18.
now let's start solving 2 times 12 is 24
2 times 6 is 12 plus 2 times 18
is 36. so the top
or i'm sorry the front and back combined
we have an area of 24 square inches the
right and left combined area of 12
square inches
and the top and bottom has a combined
area of 36 square inches
so we have all of our faces included
now we just need to add everything
together so surface area
equals 24 plus 12 is 36
plus 36 gives us an answer of 72
square inches so that's the area of all
of the faces
added together so there you have it
there's how you find the surface area of
a rectangular prism
again find the area of each face
and then add all of that together i hope
that helped
thanks so much for watching until next
time
peace
![Surface Area of a Rectangular Prism - [7-6-15]](https://i.ytimg.com/vi/9q_x6Y8fLl4/mqdefault.jpg)
