hi welcome to math antics in this lesson
we're gonna learn about an important
concept in geometry called perimeter
perimeter is just a fancy math term that
means the distance or length around a
shape but what exactly does the distance
around a shape mean well distance or
length is a one-dimensional quantity
that we can measure with units like
centimeters inches or miles that means
that perimeter is also a one-dimensional
quantity that we can measure with units
of length for example the perimeter of a
shape wouldn't be just 10 but it could
be 10 centimeters or instead of being
just 25 it could be 25 miles the units
are really important when you're talking
about perimeter okay but what exactly do
we mean by around a shape seems like
there would be a lot of different ways
to go around a shape some of them would
be short and some of them would be very
long well perimeter means the absolute
shortest distance possible around a
shape that would be the distance you'd
get if you trace the path exactly around
the border or edge of a shape a good way
to see what perimeter is is to imagine
that you could walk right along the edge
of a shape like this five sided polygons
imagine starting at one of the polygons
vertices and then walking along each
side until you got all the way back to
the point that you started from the
total distance you traveled would be the
perimeter of that shape in this case if
the length of each side of the polygon
was 10 meters the total length you would
travel along all five sides would add up
to 50 meters another good way to see
what perimeter is is to imagine that you
could take a shape like this square and
break it at one of its corners then you
could unfold the shape until it formed a
straight line the length of that line is
the perimeter of the shape doing this
helps you understand why perimeter is a
one-dimensional quantity even though it
applies to two-dimensional shapes like
this square it's one dimensional because
it's the distance of the lines that go
around the
dimensional shape okay so now that you
know what parameter is how do we measure
or calculate it for different geometric
shapes well that depends on the shapes
finding the perimeter of shapes that
have curves like circles or hearts or
things like that can be tricky
in fact we'll wait and talk about the
perimeter of a circle in another video
in this video we're just going to focus
on how to find the perimeter of polygons
since polygons are made from only
straight sides it's easy to find their
perimeter if you know the length of each
side all you have to do is add them up
and the total length you end up with is
the perimeter of the polygon let's try
doing that with a few examples so you
see how it works the first polygon we'll
try is a triangle this triangle has
three sides that are each a different
length 3 centimeters 4 centimeters and 5
centimeters now to find the perimeter of
the triangle all we have to do is add up
the lengths of those three sides three
plus four plus five equals 12
but don't forget it's not just 12 it's
12 centimeters always remember to also
put down the units of the perimeter okay
that was easy let's try another one
this time our polygon is a rectangle and
you can see that the shorter sides are
each 5 meters long and the longer sides
are each 10 meters long so let's add
them all up we can add up the sides in
any order we want to as long as we don't
forget any sides or accidentally count
any of them twice and I think I'll add
up the two short sides first 5 plus 5
equals 10 next all add up the two longer
sides 10 plus 10 equals 20 and now if I
add up those two answers I'll get the
total for all four sides 10 plus 20
equals 30 so the perimeter of this
rectangle is 30 meters you thought I was
gonna forget my units 10 of you not this
time ah here's another good example this
is a six-sided regular polygon a regular
polygon means that all its sides are
exactly the same length and that's good
because this diagram only shows the
length of one
side for centimeters but since the
polygon is regular we know that all the
other sides are also four centimeters
long now we could just add up all the
sides like we did before but since
they're all the same we can use
multiplication as a shortcut
that's because multiplication is really
just repeated addition all we have to do
is multiply the number of sides six by
the lengths of the sides for centimeters
six times four equals 24 so that means
the total perimeter must be 24 24 what
centimeters that's better oops and this
formula works for any regular polygon no
matter how many sides are if the sides
are all the same length you can just
multiply the number of sides by the side
length and you have the perimeter okay
let's try one more example this polygon
also has six sides but it's not a
regular polygon the sides are different
lengths and this one's really tricky
because they only show is the length of
four of the sides the other two are
missing so how can we figure them out
problems like this come up all the time
in math problems where you aren't quite
given all the information when you have
this kind of problem the key is to use
what you do know to figure out what you
don't know here's what I mean look
closely at the two vertical sides that
we do know the lengths of four inches
and six inches now imagine that those
two vertical sides could be moved
straight across to the other side the
side that we don't know the length of by
doing that you can see that the missing
length would just be the combination of
the two vertical lengths that we do know
4 inches and 6 inches and since 4 plus 6
equals 10 the missing vertical side must
be 10 inches long notice that we can do
the same thing for the horizontal sides
that we do know if we imagine those
moving down to the side that we don't
know we see that it's length must be
equal to the combination of those two
lengths 10 inches plus 5 inches equals
15 inches there we've used the lengths
that we did know to figure out the
lengths that we didn't know and now that
we know the lengths of all the sides we
can just add them all up to get the
perimeter
4
five plus six equals fifteen and then 15
plus 15 equals 30 30 plus 10 equals 40
and last of all 40 plus 10 equals 50 so
the sum of all the sides is 50 inches
and that's the perimeter of this shape
and that's the end of this lesson we've
learned that perimeter is the distance
or length around a geometric shape and
we've learned how to calculate it for
any polygon you just add up the lengths
of all the sides and the total length is
the perimeter oh and don't forget your
units also don't forget that to get good
at math takes practice thanks for
watching math antics and I'll see you
next time learn more at math antics comm