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welcome to math with mr j
[Music]
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
