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- anonymous

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- anonymous

ABCD is a parallelogram
Which is greater
a. The area of ABCD
b. 24 |dw:1437774703693:dw|

- freckles

do you know how to find the area of parallelogram ? |dw:1437775012406:dw|

- freckles

where the area is b*h

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## More answers

- freckles

we are actually given b is 4

- freckles

can you find h?

- anonymous

how do i find h?

- freckles

you could use a trig ratio
you know an angle and you also know the hyp of the triangle I drew inside the parallelogram

- freckles

the opp of that angle is the thing you want to find

- freckles

opp and hyp
think sin( )

- anonymous

wait.... I cant use sin we don't use that it has to be an alternative method...

- freckles

ok what is the alternative method?

- anonymous

im not sure it has to be done without sin tho...

- freckles

oh then I don't know of another way to find the area

- anonymous

crap... it's talking about the area of the parallelogram is equal to the length of base AD which is 4 times the height which is less than 6

- freckles

ok

- anonymous

Since the product of 4 and a number less than 6 must be less than 24, the area of the parallelogram must be less than 24.

- freckles

so we don't need to find the area exactly

- freckles

we can approximate it

- anonymous

what does this all mean..

- anonymous

24

- freckles

right 4*h<24

- freckles

where 4*h is the area of the parallelogram

- freckles

didn't label what I called a by the way
|dw:1437775996191:dw|
I used Pythagorean theorem

- freckles

\[6^2=h^2+a^2 \\ 6^2-a^2=h^2 \\ \sqrt{6^2-a^2}=h\]

- anonymous

hmmmmm i think i get it now..

- freckles

and I wanted the thing inside the square root to be positive
and I also want a to be positive because a represents a measurement

- anonymous

ok

- freckles

and if we multiply both sides by -1
we have
\[-6<-a<0 \\ \text{ so back to the inequality } \\ 4 h=4 \sqrt{36-a^2}<4 \sqrt{36-0^2}\]

- freckles

but yeah I would have used my trigonometry knowledge :p

- anonymous

this is complicated I'm gonna sit and stare at this for a while.

- freckles

\[4h=4 \cdot 6 \sin(55)=24\sin(55) \approx 19.66 \]

- freckles

all you have to know is that since h is between 0 and 6 (not including 6)
we have 4h<4(6)

- anonymous

hmmm... ok got it

- freckles

how about we say something in general...
|dw:1437776683255:dw|
so the simplest way I can write this for your problem is:
|dw:1437776770728:dw|

- freckles

and we know a>h because in the right triangle we drew we have a is the hyp
or in your example 6 is the hyp

- freckles

anyways I think I'm done now :)
unless you have questions

- anonymous

ohhhh okay i think i understand better now

- anonymous

needed that visual thank you ^_^

- freckles

visuals are the secret to math

- anonymous

agreed!!

- freckles

I think it helps to know the hyp is the longest side in a right triangle on this question

- anonymous

yea definitely helps

- freckles

but in all fairness to you
I think I started with a complicated reason
but the last reason I gave I think is definitely less complicated

- anonymous

yea it helped towards the end thanks again =)

- freckles

np

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