Why is the area of a triangle 1 2bh
1/2 bh: Alternative Formula for Area of a Triangle
an alternative formula for the area of a
triangle so far we've used the formula
base times height divided by two you may
also see this written as the H over to
be an H written together like this means
base times height this is a perfectly
good formula and it always works but
have you noticed something as you've
been doing your practice if we do this
one base times height 4 times 6 is 24
now that we've done the multiplication
step do you feel like just jumping to
the area value without writing the
divided by 2 step we know the area is 12
centimeter squared because we can half
24 in our heads if you do this you're
building math muscle and you're ready
for more we'll put this over here and
get a duplicate triangle cut it in half
down the middle if I flip this part over
we can put it back together and make a
rectangle we just have the original base
of 4 centimeters the height is still 6
and 2 times 6 gives an area of 12
centimeters squared done in one line I
have the base before multiplying and
this always works we can write a new
formula to describe this math
half base times height math textbooks
show this as half B H we don't meet this
formula first because some people find
it a bit confusing when written this way
I don't want you to be confused but I do
want you to know that you might see it
like this as well and if you do you know
what it means let's do another one here
we've got a base of three and a height
of four you might say to me I don't want
to do half of three because that's one
point five do you think I'm crazy why
would I make it difficult like that and
that would be a perfectly fair response
but get this you can keep the base and
half the height instead now that makes a
difference doesn't it why can we do this
if the formula says half the base times
the height two reasons any side of a
triangle can be considered as the base
so we can decide that this is the base
and this is the height and also you know
that the audio multiply numbers doesn't
matter you always get the same answer so
you can have either the base or the
height and the result is the same
of course I'm not having this base you
know why I'm harming the height instead
half of 4 is 2 base times half the
height then 3 times 2 is 6 centimeters
squared
it's quicker than the base times height
over 2 formula
this is the alternative formula at work
but is not the shortcut I promised you
last time that's coming next and it's
actually in the original formula here's
my triangle and we're all ready to go we
know we can divide either base or height
by two do you remember multiplying
fractions and reducing before we
multiply
wellman here comes the shortcut we can
just divide by two like reducing a
fraction so 2 divided by 2 is 1 and 12
divided by 2 is 6 and now 5 times 6 is
30 centimeters squared
how quick is that in fact this is the
easiest way to get the area of a
triangle use it if either the base or
the height is an even number so it can
be half easily set out for the original
formula and reduce either base or height
not both by this factor of 2 and of
course that gets rid of the denominator
then just multiply and there's the area
one line of math only nice this strategy
is particularly helpful if you have a
triangle like this one base is 7 times
height of 24 do we really want to
multiply 7 by 24 course not
do it the easy and quick way instead
divide straight away just like you do
for fractions multiplication and we get
7 times 12 that's 84 so the area is 84
centimeters squared how about that for a
time-saver you are now ready to rock any
area of a triangle question and you now
have several strategies you can use have
fun see you soon
