How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)

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- Feb 5th 2006, 02:53 PMextreme_pitriangles are evil!
How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)

- Feb 5th 2006, 04:27 PMticbolQuote:

Originally Posted by**extreme_pi**

1) Get the lengths of the 3 sides by distance between two points (x1,y1) and (x2,y2) is sqrt[(x2 -x1)^2 +(y2 -y1)^2]. Then use the Heron's formula. One way.

2) Enclose the triangle by a rectangle. Area of triangle equals area of rectangle minus the areas of the 3 right triangles enclosing the said triangle. Way #2.

3) Get the 3 altitudes. Then area = (1/2)(altitude)(base). Ways #3,4,5.

4) Get the 3 interior angles. Then area = (1/2)(side)(another side)*sin(included angle). Ways #6,7,8.

5)Get the inradius. Then area = (1/2)(inradius)(perimeter of triangle). Way #10.

6) Then there is one formula using the circumradius. Way #11.

Many more, maybe, but cannot concentrate on them now....

The Living Deads (aka The Rolling Stones) just finished spooking the festivities. Second Half of the Game coming up. See ya later... - Feb 5th 2006, 05:02 PMThePerfectHackerQuote:

Originally Posted by**extreme_pi**

having sides, $\displaystyle a,b,c$

Then its area is,

$\displaystyle A=\sqrt{s(s-a)(s-b)(s-c)}$

Now to find the length of the sides of the triangle you can use the distance formula. It states that the distance between points $\displaystyle (x_0,y_0)$

and $\displaystyle (x_1,y_1)$ is:

$\displaystyle d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}$

And it does not matter which one is which.

Here is a picture. - Feb 5th 2006, 06:07 PMticbolQuote:

Originally Posted by**ticbol**

MAN !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

ZEEZZZZZZZZZZZZZZZZZZ!!!!

WE GOT IT!!!!!!!! - Feb 5th 2006, 06:53 PMextreme_pi
YEAHHH Steelers win!!!!!!!!!!!!!!!!!!!

Now I can get on with my actual life! - Feb 5th 2006, 09:53 PMticbolQuote:

Originally Posted by**extreme_pi**

CONGRATULATIONS!

Search the Web re "Steelers" or "Steelers Nation" and we'd be in heaven for a long, long time.

ticbol

{aka Cowher or Ward or Porter or Bettis or Polamalu or Roethlisberger or ..... for a while, from now on.} - Feb 9th 2006, 06:16 PMThe PondermaticThank you thank you thank you thank you thank you thank you
Thanks for the image and the formula, ThePerfectHacker. They should help me out, as I am working on the exact same project. :)

BTW, I don't care about football very much. I did host a Super Bowl party, but I did it more to show off my Dance Dance Revolution skills than to watch football. :p The Steelers won. So.