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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 volume of a triangular prism

now remember the volume is the amount of

space an

object takes up and for any prism

we can use the formula the area of the

base

times the height so again the volume for

any prism

is the area of the base times the height

that capital b means the area of the

base and that

h stands for height now since we're

working with

triangular prisms we're going to have

triangular bases

so to find the area of those triangular

bases

we use the formula base times height

divided by two

the formula for the area of a triangle

so this is a more

specific formula over here for

triangular prisms again because we're

using the formula for the area of the

triangular bases base times height

divided by two

and then we multiply that by the height

of the prism

so let's jump into number one and take a

look at the bases of that

triangular prism now the bases of a

prism are congruent

and parallel polygons in the case of

triangular prisms we're going to take a

look at the triangles

that are congruent and parallel so for

number one that triangle up front

is congruent and parallel to the

triangle

in the back now we can't see that full

triangle in the back

but it is congruent and parallel so

congruent means

same exact size and shape now we

name prisms by their bases that's why we

call this a triangular prism because our

bases

are triangles now the height is going to

be the distance

between those bases the height isn't

necessarily going to be vertical or up

and down

again it's defined by the distance

between those bases

so let's find the volume of number one

and we'll start by writing out

our formula so volume equals

base times height divided by 2 which is

the formula for the area of a triangle

times the height of the prism let's plug

in

so volume equals well base of the

triangle is five centimeters

so we'll plug in five

times the height of the triangle is four

centimeters

and let's divide by 2

and multiply by the height of the

prism not the height of the triangle we

need to find the height of the prism

so that's going to be 6 centimeters

let's solve so 5 times 4 is

20 divided by 2 is

10. so that's the area of

our triangular base 10 times

6 is going to give us 60. so

volume equals 60

cubic centimeters again i did

5 times 4 which is 20 divided by 2

is 10 times 6 is

60. so our final answer is 60 cubic

centimeters

so let's move on to number two and we'll

start by writing out

our formula so volume equals

base times height divided by 2

times the height of the prism now we

plug in

so the base of our base the triangular

base is going

to be 10 inches right here so we'll plug

in

10 times the height

which is 7 inches divided by 2.

now the height of the prism the distance

between

the two bases is going to be three

inches

so we multiply it by three so we end up

with

10 times seven which is 70

70 divided by 2 is 35

so we need to solve 35 times 3

and if we can't solve that using mental

math that's okay

come to the side in order to work

through

that problem so let's do 35 times three

up here to make sure we get the correct

answer

three times five is fifteen

three times three is nine plus one is

ten so we get

105. so our volume

is 105 cubic

inches and we are done

to recap we did 10 times 7 is

70 divided by 2 is 35

and then we did 35 times 3

that 3 is the height of the prism and we

got

105. so our final answer volume equals

105 cubic inches

so there you have it there's how you

find the volume of a triangular prism

take the area of our triangular base and

multiply it by the height of the prism

so i hope that helped thanks so much for

watching

until next time peace