hey there it's Kalei in this lesson we will learn how to find the area of
parallelograms and trapezoids let's get started do you remember how to find the
area of a rectangle we can use a formula that says the area is equal to the
length times the height on this rectangle the length is 6 and the height
is 2 so we would multiply those together to get 12 now what about finding the
area of a parallelogram notice that the parallelogram is similar
but because the sides are angled we can't use the same formula and multiply
side lengths as the height we need to know the actual height of the
parallelogram since we have a grid we can count the height by counting the
squares 1 2 and we see the length is labeled as 5 but I only count 1 2 3 4
whole squares but notice that these partial squares over here and these ones
over here make up a full square so in fact I do have 5 square lengths so now
we can multiply length times height 5 times 2 is 10 are you curious about how
we can use the same formula for a parallelogram and a rectangle or a
square well imagine this you have a square with a height of 10 and a length
or a width that's also of 10 and that gives you when you multiply them
together an area of 100 now if you have a parallelogram that also has a length
or width down here of 10 and then tells you that the height here is 10 but
you're not sure how long this side length is you know that that's okay
because the formula is the same you multiply the width or the length down
here times the height and to see how that would be true we can drag the
corner from our parallelogram over here and if we drag it over and
it over here we see that we have the same shape as this 10 by 10 square so
that's how a parallelogram and a rectangle can share the same formula for
area let's find the area of this parallelogram using our formula area
equals base times height so I know my base is this distance down here
measuring it seven feet and I see that my height is this measurement here
notice it's not the same as my side link and there this 3 feet so I can say area
is equal to 7 feet my base times 3 feet my height and that will give me 21 I
have to square my unit square feet and there we have it now that we know how to
find the area of rectangles and parallelograms let's look at trapezoids
now looking at these three shapes can you think of a way that we can compose
or manipulate the trapezoid to calculate its area so here I have one trapezoid
and you can see the different dimensions I have my top up here my bottom down
here and the height of my trapezoid now watch as I compose the trapezoid into
another shape so I'm taking now two trapezoids I'm going to rotate one of
them and when I put it together I've composed a parallelogram so now I have a
parallelogram and I know how to find the area of a parallelogram it's a is equal
to base times height and here I know my height already is
seven but what's my base it's this line here Plus this line here but I know what
the distance is here because it's the top from my purple trapezoid so that's a
six so if I wanted to find the area of this parallelogram I would have my base
would be the base of one this up here plus the base of two this one down here
and I have to multiply all of that by my height and that would
give me the area of this entire parallelogram but now what if I only
want the area for one trapezoid well one trapezoid is half the area of
my parallelogram right because this is made up of two trapezoids so I take this
area that I've just created for this parallelogram where I add my two bases
together and I would divide it by two so now I that have area is equal to b1 plus
b2 times the height all over 2 now let's find the area for this trapezoid using
the formula we derived that says area is equal to base one plus base 2 times the
height all over 2 so we can see here that we have two bases one down here
measuring at six inches and one up here measuring at two inches and then we have
our height right here coming in at our right ankle all right so we can say area
is equal to six inches plus two inches all times four inches divided by two so
we do our order of operations parentheses go first six inches plus two
inches that gives me eight inches 8 inches times four inches all over two so
I have eight inches times four inches eight times four gives me 32 I have to
multiply my units together so I mean gives me inches squared or square inches
all over two and now 32 divided by two that gives us 16 square inches as our
area great job now you know the formulas for finding area in parallelograms and
trapezoids practice what you've learned by doing the online games and quizzes
have fun and remember to always be clever