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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