area of parallelograms, triangles, and...

AREA FORMULAS 1 © 2009 AIMS Education Foundation

Parallelogram Cut-UpsTHINGS TO LOOK FOR:

A R E A O F P A R A L L E L O G R A M S , T R I A N G L E S , A N D T R A P E Z O I D S E S S E N T I A L M A T H S E R I E S

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1. What do you know about the sides of a parallelogram?

2. How do you find the perimeter of a parallelogram?

5. What is the formula for finding the area of a parallelogram?

3. What is the base of a parallelogram?

4. How do you find the height of a parallelogram?

Like forparallelogram C,it was 12 plus 16plus 12 plus 16.

that’s 56.

The measuring pad was like two rulers thatwere perpendicular to each other. It waseasy to put one side of a parallelogram on

one of the rulers and measure it.

I justmultiplied the

long side and theshort side eachby 2 and thenadded them!

Okay, how manysides did you have

to measure?

That’s right,mark. For every

parallelogram, thesides across from each

other are not onlyparallel, but they

are also equalin length.

We callthem opposite

sides. So, we cansay that opposite

sides of aparallelogram

have equallength.

What elsedid you do?

After measuring,we added up the lengthsof the four sides to find

the perimeter.

The perimeteris how far it is

around theparallelogram.

It waspretty far.

After you cut out theparallelograms atthe beginning of thisactivity, you measuredsome lengths. Let’stalk about that.

Yeah, we measuredthe sides. We usedthis pad thing tomeasure them.

We only needed tomeasure two sidesbecause the sidesthat are acrossfrom each otherare the samelength.

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12 + 16 + 12 + 16 = 56

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Measuring Pad


2

Well done. Either way

is fine for findingthe perimeter.

The next thingwe did was to findthe area of each of

the parallelograms,right?

Well, we firsthad to measure

the heights of theparallelograms.

For eachbase there isa height thatgoes with it.

Hold on aminute, vanessa,

that is a very goodobservation.

Wait, now theheight changed.

It’s not 12anymore?

Well, yeah,red, that’s

prettyobvious.

Yeah, Red,things changewhen you use

a different sidefor the base.

The perimeter forparallelogram C

was 2 times 12plus 2 times 16.

using the pad, we rested one of the sides of theparallelogram on the bottom ruler and measured

the height of the perpendicular dotted line.

Like if parallelogram C is resting on thelong side, then that’s the base and that’s 16. If

you measure the height from that base it’s 9.

So, whenparallelogram C isresting on the shortside, the height is12. Now we knowhow tall it is!

I get it, theparallelogram istaller when it’sresting on the shortside, and it’s shorterwhen it’s resting onthe long side.

Yeah, and whatever sidethe parallelogramis resting on, we

call that thebase.

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Does thatmean we have to

know two differentformulas for the area

of a rectangle?

And I wantedto show you how

that helped us finda formula for finding

the area of anyparallelogram.

It’s becausewe already knew

the formula to findthe area of arectangle.

So, class, howdid we do it? How did

we figure out theformula for finding

the area of anyparallelogram?

But right now,we can use base

times height to helpus figure out a

formula for thearea of any

parallelogram.

We just cut upthe parallelogram

and put it backtogether to make

a rectangle.It was fun!

And theparallelogram

and the rectanglehave the same area

because they’re bothmade out of thesame pieces.

We foundout that anotherway to think about

the formula for areaof a rectangle is

that it’s basetimes height.

That’sexactly right,

Mark.

What we found out was that length and widthon a rectangle are the same thing as baseand height. So, a rectangle has a base and

height just like all the rest of theparallelograms.

If 12 is the base of the rectangle, thenthe height is 8, right? And the area is base times

height, that’s 12 times 8 or 96.

Class, there is animportant reasonwhy we included therectangle alongwith the other twoparallelograms.

Not really, redmond. You’ll usually thinkabout the area of arectangle as lengthtimes width.

Yeah, we already knewthat the formula forfinding the area of arectangle is lengthtimes width.

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Is that theformula for the areaof a parallelogram?Is it base times height

for everyparallelogram?

And you canuse the short sidefor the base or youcan use the long

side, right?

That is an excellentsummary, redmond.

You’ve got it!

That’s right,juana. You just haveto be sure that youmeasure the heightfrom that base.

But for aparallelogram thearea is just base

times height.

I think I’vegot it! The area of

the rectangle is lengthtimes width or base

times height! They meanthe same thing,

right?

So, if base timesheight tells us the

area of the rectangle,then base times heighttells us the area of

the parallelogramas well!

Like for parallelogram C, if we cut it up intotwo pieces, we can move that triangle to the

other side and it makes a rectangle.

You can turn the parallelogram into arectangle and both shapes have the same base

and height. They also have the same area.

The same thinghappens when you cutup parallelogram B.

The area of therectangle is basetimes height, or 9

times 16, same as theparallelogram.

So, if the area of therectangle is basetimes height, thenthe area of theparallelogram isbase times heightas well.

It is,redmond.

For everyparallelogram, if you

measure one of the sides, that’scalled the base. And if you then

measure the height from thatbase, then the area is base

times height.

C9

16

C

9

16

C

9

16

C

9

16

B8

9

B8

9

B8

9

h

b

area of parallelograms, triangles, and...

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