1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Area of irregular square

  1. Dec 10, 2011 #1
    Hi,

    How do you solve for the area of irregular square. What's the formula? For example. A square has the following 4 sides:

    side a: 11.83 meters
    side b: 38.74 meters
    side c: 12.00 meters
    side d: 36.02 meters

    What is the total area? Thanks.
     
  2. jcsd
  3. Dec 10, 2011 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Well, it is not a square, and you need to know the angles.

    I guess it's trying to be a rectangle if a is opposite c, and the angles are as close as possible to right-angles.
    Then the shape will cover the maximum possible area for the sides - this what you mean?
    Or do you mean any old tetragon?
    http://www.mathopenref.com/tetragon.html
     
    Last edited: Dec 10, 2011
  4. Dec 11, 2011 #3
    The area of an irregular quadrilateral is

    [tex]A= \sqrt{(s-a)(s-b)(s-c)(s-d)-abcd\cdot\cos^2{\frac{\alpha +\gamma}{2}}}[/tex]

    where a,b,c,d are the sides. s is the semi-perimeter and [itex]\alpha[/itex] and [itex]\gamma[/itex] are any two opposite angles.
     
  5. Dec 11, 2011 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    @Blandongstein: awesome first post, welcome to PF.
    Unfortunately we are not supplied with any angles ... so more information is needed from stglyde.

    I was intrigued by the description as a "irregular square" ... another common formulation is to inscribe the tetragon/quadrilateral inside a circle for example. If we know the constraints on how squashed the shape can be, we can answer the question.
     
  6. Dec 11, 2011 #5
    I just want to get the approximate area and I think it is easy by simply multiplying 12 x 37 or 444 so I'm satisfied. Thanks for the help.
     
  7. Dec 11, 2011 #6

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    There you go you see - not enough information was supplied.
    The area must be pretty close to rectangular for that approximation to work.
    But if, say, the angle between side a and side b is small, then a better approximation would be for a triangle. See why you got such complicated answers?

    Oh well. Good luck.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook