SOLUTION: triangle has coordinates A(-5, 1) B(-2, 5) and C(1,1). Find the area of the triangle and its perimeter. Please answer by tonight I have a quiz tomorrow

Algebra ->  Triangles -> SOLUTION: triangle has coordinates A(-5, 1) B(-2, 5) and C(1,1). Find the area of the triangle and its perimeter. Please answer by tonight I have a quiz tomorrow      Log On


   

Question 490090: triangle has coordinates A(-5, 1) B(-2, 5) and C(1,1). Find the area of the triangle and its perimeter.
Please answer by tonight I have a quiz tomorrow
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
We can use the distance formula to find the area between coordinates.
sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29
AB = sqrt%28%28-2+-%28-5%29%29%5E2+%2B+%285+-+1%29%5E2%29
AB = sqrt%2825%29 = 5
BC = sqrt%28%281+-+%28-2%29%29%5E2+%2B+%281+-+5%29%5E2%29
BC = sqrt%2825%29 = 5
AC = sqrt%28%281+-+%28-5%29%29%5E2+%2B+%281+-+1%29%5E2%29
AC = sqrt%2836+%29 = 6
So this will give us the length of the sides
AC = 5
BC = 5
AC = 6
The perimeter therefore will be 5 + 5 + 6 = 16
The area we can find using Herons formula.
Area = sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29
Where s is the semiperimeter of the triangle.
s = 5 + 5 + 6/ 2 = 8

sqrt%288%283%29%283%29%282%29%29
Area = sqrt%28144%29
Area = 12
A good website that explains this formula is:
http://www.mathsisfun.com/geometry/herons-formula.html
Cleomenius.