• Status: Solved
  • Priority: Medium
  • Security: Public
  • Views: 322
  • Last Modified:

Calculate the Area of a Triangle

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

http://www.clothier.org.uk/picture1.jpg

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

Many Thanks
0
jclothier
Asked:
jclothier
  • 3
  • 2
  • 2
2 Solutions
 
oceanbeachCommented:
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

therefore:

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

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



0
 
ozoCommented:
Didn't I ansqwer this before?
L=sqrt(A²-(C/2)²)
R=(4(B-L)²+C²)/(8*(B-L))
A=R²arcsin(C/(2R))+C(L-sqrt(R²-(C/2)²))/2
0
 
oceanbeachCommented:
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.
0
Concerto's Cloud Advisory Services

Want to avoid the missteps to gaining all the benefits of the cloud? Learn more about the different assessment options from our Cloud Advisory team.

 
jclothierAuthor Commented:
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.

 L=sqrt(D²-(W/2)²)
R=(4(Z-L)²+W²)/(8*(Z-L))
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!
0
 
oceanbeachCommented:
jclothier,

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!
0
 
ozoCommented:
sin¯¹(x) is a notation for arcsin(x)
which can be confusing, since it looks a lot like sin²(x)
0
 
jclothierAuthor Commented:
Thanks for clearing that up ozo.
0

Featured Post

Concerto Cloud for Software Providers & ISVs

Can Concerto Cloud Services help you focus on evolving your application offerings, while delivering the best cloud experience to your customers? From DevOps to revenue models and customer support, the answer is yes!

Learn how Concerto can help you.

  • 3
  • 2
  • 2
Tackle projects and never again get stuck behind a technical roadblock.
Join Now