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Math Help - Area of a triangle

  1. #1
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    Area of a triangle

    Use calculus to determine the area of the triangle give the verticies

    (0,5) (2,-2) (5,-1)
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    Quote Originally Posted by treetheta View Post
    Use calculus to determine the area of the triangle give the verticies

    (0,5) (2,-2) (5,-1)
    use calculus? what class are you in? there are many simple geometric ways to do this. i can't think of any real calculus ways, unless you want to use vectors or something
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    We have to use Integrals, and it's First year calculus course

    if you don't mind can you show me the vectors way as well
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    Quote Originally Posted by treetheta View Post
    We have to use Integrals, and it's First year calculus course

    if you don't mind can you show me the vectors way as well
    oh, ok, duh!

    have you drawn the triangle? do you see what functions it is bounded by? they will be straight lines

    you will need two integrals
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    Yah I have, I just don't get how to integrate with the equation's like from what to what

    I know I should be using the intersects but there's 3 intersects and I think I only need to use 2 of them
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    Quote Originally Posted by treetheta View Post
    Yah I have, I just don't get how to integrate with the equation's like from what to what

    I know I should be using the intersects but there's 3 intersects and I think I only need to use 2 of them
    see the pick below. the desired area is given by A = \int_0^2 [f(x) - g(x)]~dx + \int_2^5 [f(x) - h(x)]~dx. i leave it to you to find f(x) ,~g(x) \text{, and }h(x)
    Attached Thumbnails Attached Thumbnails Area of a triangle-points.bmp  
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    Yah see I knew I had to do 2 integrals

    how did you know it had to be from 0,2 and 2,5
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    Quote Originally Posted by treetheta View Post
    Yah see I knew I had to do 2 integrals

    how did you know it had to be from 0,2 and 2,5
    recall that we find area of a bounded region by integrating the top function minus the bottom function. f(x) is always on top, but g(x) is the bottom function between x = 0 and x = 2. similarly, h(x) is the bottom function from 2 to 5. the points we were given are our guides.
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    You are one smart cookie (:
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