# Area of irregular square

#### stglyde

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.

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#### Simon Bridge

Homework Helper
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:

#### Blandongstein

The area of an irregular quadrilateral is

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

where a,b,c,d are the sides. s is the semi-perimeter and $\alpha$ and $\gamma$ are any two opposite angles.

#### Simon Bridge

Homework Helper
@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.

#### stglyde

@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.
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.

#### Simon Bridge

Homework Helper
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.

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