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


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


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