Heres a toughy...

Find the area of the region defined by the following inequalities.

$$y \ge-4x-16$$

$$4y \le26-x$$

$$3y+6x \le30$$

$$4y-2x \ge-10$$

pleaseee

Question

Heres a toughy...

Find the area of the region defined by the following inequalities.

$$y \ge-4x-16$$

$$4y \le26-x$$

$$3y+6x \le30$$

$$4y-2x \ge-10$$

pleaseee

anonymous · Answer

wow. so far i have managed a picture. i guess we need the corners but what a lot of work! http://www.wolframalpha.com/input/?i=graph+++y%3E-4x-16+and+4y%3C26-x+and+y%2B2x%3C10+and+2y-x%3E-5

anonymous · Answer

i know right? its due tomorrow. i have 3 of the lines graphed, but do you have any idea how to find the area?

anonymous · Answer

not a clue

anonymous · Answer

fml.. lol thank you though

anonymous · Answer

i had a n idea of putting a rectabgle around it and then finding the triangles that arents part of the inequalities solution? would that work? im not sure if that what you suggested

anonymous · Answer

i found the corners if that will help

anonymous · Answer

yea, i think it might. at least its something to try

anonymous · Answer

starting in the picture i sent from top left, and going counter clockwise they are 
(-6,8)
(2,6)
(5,0)
(-3,-4)

zarkon · Answer

75

anonymous · Answer

what tools do you have at your disposal? you could divide it up into two triangles and use heron's formula, or perhaps trig.  will take a while.  is there some formula you are supposed to use from a book, or is this just to keep you busy for a few hours?

anonymous · Answer

zarkon? how do you know?

zarkon · Answer

I cheated

anonymous · Answer

somehow i knew zarkon would get it.  explanation??

anonymous · Answer

how though?

anonymous · Answer

maple?  mathematical?

zarkon · Answer

I did it all on my calculator

anonymous · Answer

i have a TI-84 plus, im sure i could too. can you tell me how?

zarkon · Answer

drew the inequalities...created a polygon...asked calculator to calculate area :)

anonymous · Answer

what?! what kind of calculator is that?

zarkon · Answer

my Ti-Nspire CX CAS

anonymous · Answer

ooooh =/

zarkon · Answer

http://www.mathopenref.com/coordpolygonarea.html

anonymous · Answer

wow check this out!!

anonymous · Answer

what is itt?

anonymous · Answer

75 it is! http://www.mathopenref.com/coordpolygonarea.html

zarkon · Answer

yes...my calculator rules   ;)

anonymous · Answer

haha yes it does.. how much is it?1

zarkon · Answer

about 150 us

anonymous · Answer

well it was when i dragged them but it doesn't save it.  drag the points and you get it.  i just did in on line on the link zarkon sent

anonymous · Answer

yea i see it, thank you guys!

zarkon · Answer

Decided to post the output from my calc  :)