Calculate the Area of a Triangle

Posted on 2006-04-01
Last Modified: 2010-05-19
Hi All

I need a formula to calculate the area of a trinagle, but theres a twist. The triangle as a curved face. Heres a picture of what I am talking about

I need to calculate the area using only the dimmensions specified on the drawing, A, B & C.

Many Thanks
Question by:jclothier
    LVL 12

    Expert Comment

    Iknow you could do this with calculus, but thinking simpler, this is a sector of a circle.

    Area of a circle = Pi*r^2.

    Area of a secotor of a circle = 0.5*r^2*x

    angle of sector = x = 2z

    r = a = b

    sin z = a/(0.5*c)

    z = sin^-1(a/(0.5*c))

    x = 2*(sin^-1(a/(0.5*c))) = angle of sector of circle


    Area of a secotor of a circle = 0.5*r^2*x

    = 0.5*r^2*(2*(sin^-1(a/(0.5*c))))

    LVL 84

    Accepted Solution

    Didn't I ansqwer this before?
    LVL 12

    Assisted Solution

    oops, r = a = b....

    Area = 0.5*a^2*(2*(sin^-1(a/(0.5*c))))

    Also, I assumed the angles created by the intersection of lines b & c to be 90 degrees.

    the drawing is a sector of a circle.  is is also 2 identical sectors of the same circle.  I used one of the triangles created by these 2 identical sectors of the same circle to find the corresponding angle.  This angle was doubled to find the angle of the original sector (hence, x = 2z).

    It has been a while, but I think this is correct.

    Author Comment

    Thanks to both of you.

    Oceanbeach, The angle is not always going to be 90 degrees and it also is not always going to be a sector of a circle. The formula that you have given is correct based on that so I have awarded you some points.

    ozo, Yes you have answered this for me before but after I accepted I couldn't get the formula to work.

    A = (R²sin¯¹(W/(2R))+W(L-sqrt(R²-(W/2)²))/2)

    I think that the problem was with this part sin¯¹

    I note that this time you have changed it to arcsin

    This may just be not knowing what I am talking about but this made it work.

    Thanks again!
    LVL 12

    Expert Comment


    You know what they say about assumptions....

    Aside from bad assumptions, I am glad my thought process was correct.  I sure hope I at least helped since you gave me an assist.

    Happy number crunching!
    LVL 84

    Expert Comment

    sin¯¹(x) is a notation for arcsin(x)
    which can be confusing, since it looks a lot like sin²(x)

    Author Comment

    Thanks for clearing that up ozo.

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