How many ways are there to find the area of a triangle with coordinates of (-11,0),(0,7),(15,-13)
Plenty. I do not have all the time now because my attention is on the Super Bowl XL (it's halftime now, my team, Steelers, leading 7 to 3. Zeez, we are just lucky. Our quarterback is nervous. But I see that when the 2nd half resumes, he will explode, meaning, wake up, and he'll kill 'em Seahawks. Man!).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...
You can use Heron's Formula, if the semiperimeter of a triangle is $\displaystyle s$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.
Whoa, you are one of us too? Steelers Nation? Man!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.}
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. The Steelers won. So.