Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
How do you find the area of this triangle?
Mathematics
jamiebookeater
  • jamiebookeater
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Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
|dw:1438116778704:dw|I need to find the area of this. How do I do that?
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
|dw:1438116845340:dw| I forgot the right angle
phi
  • phi
area is 1/2 base * height

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Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Really? That's it?
phi
  • phi
yes
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
5x3/2?
phi
  • phi
yes
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
But what about:
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
|dw:1438116970196:dw| What about that part? WHen they ask find the area which triangle am i finding it for exactly?
phi
  • phi
You found the area of the triangle. we can prove it
ChillOut
  • ChillOut
You're finding the are for the full lines one.
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
I found the area of which triangle?
ChillOut
  • ChillOut
area*
ChillOut
  • ChillOut
|dw:1438117079817:dw|
phi
  • phi
|dw:1438117108451:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh, so the |dw:1438117132170:dw| is giving me the height for the triangle?
ChillOut
  • ChillOut
Absolutely.
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh, Brainfart!
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Since I am taking geometry during summerschool I expected it to be some complicated formula. At first I ruled out that it could be that...
ChillOut
  • ChillOut
There are other formulas involving angles and stuff. But leave that for later :)
phi
  • phi
here is a proof. We assume we know the area of a rectangle is width * height |dw:1438117298679:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
So if I answer using 1/2BxH on a graded assessment it will be correct?
phi
  • phi
now put in a diagonal. the two triangles are congruent, so the area of each is 1/2 of the rectangle's|dw:1438117369207:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
So if I answer using 1/2BxH on a graded assessment it will be correct?
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
They're not expecting a different method?
phi
  • phi
now make an obtuse triangle |dw:1438117452871:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
@phi Ooh, I see. That makes sense...
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
ooh. C is the height of |dw:1438117583062:dw|
phi
  • phi
if we subtract of the small triangle on the left we are left with the obtuse triangle that is \[ \frac{1}{2} (a+b)\cdot c - \frac{1}{2} b c \\\frac{1}{2} ac + \frac{1}{2} bc - \frac{1}{2} bc \\ =\frac{1}{2} ac \]
phi
  • phi
hopefully you can follow the logic
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
I can, so you just proved 1/2BxH right?
phi
  • phi
yes, that the formula works for obtuse triangles.
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ok thanks. Can I ask another quick question?
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
How do you find the area of a kite?
phi
  • phi
1/2 the product of the diagonals http://www.mathopenref.com/kitearea.html
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Thanks!!!!
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Would the diagonals be these? |dw:1438117923899:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
phi
  • phi
the "crossbars" |dw:1438118022805:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh, ok sorry but: |dw:1438118151545:dw| It would be 1+1 x 2 + 3/2 right? @phi
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
OOps I mean 1+2 x 3+3/2
phi
  • phi
it would be except that would not be a kite (the diagonals of a kite bisect each other) see http://www.coolmath.com/reference/kites
phi
  • phi
correction: the longer diagonal bisects the shorter diagonal
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh, so what i said was right? I have a problem asking for the area where they give me the length of half of both lines.
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Like they give me this...
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
|dw:1438118486114:dw|
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
I just add the 2's and 1's and use the 1/2bxh formula right?
phi
  • phi
yes
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh ok. Thanks.
phi
  • phi
1/2 d1 * d2 (though you can think of the diagonals as the width and height)
Setsuna-Yuregeshi
  • Setsuna-Yuregeshi
Ooh, thank you so much!!!!!!!!!!!!!!

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