# A polygon with 4 sides no two of which need to be the same size?

A shape with four sizes is called a quadrilateral.

As none of them are the same size, it can simply be called an irregular quadrilateral.

If we knew more information about the shape, we could possibly categorize it further. For example, if it had a pair of parallel sides, it could be a trapezium.

### What are the properties of polygon?

A polygon is a closed plane figure that is bounded by straight sides. There may be three or more sides - up to any number. The sides can be the same size or different. It must have the same number of sides as vertices. The angles may be the same or different. The sum of the exterior angles is 2*pi radians. The sum of the interior angles of a polygon with n sides is (n-2)*pi…

### Is it possible for the interior angle of a regular polygon to be 154?

No. The sum of the exterior angles of a polygon sum to 360o For a regular polygon, they are all the same size ⇒ dividing 360o by the exterior angle gives the number of sides. Interior angle = 154o ⇒ exterior angle = 180o - 154o = 26o ⇒ number of sides = 360o ÷ 26o = 1311/13 sides But a polygon must have a whole number of sides ⇒ 154o cannot be the interior…

### How many sides does the largest polygon have?

There is no mathematical limit to the number of sides that a polygon can have. As the number of sides increases the polygon will become more and more like a closed curve - a regular polygon will become like a circle. The size of the polygon and accuracy of measurement will determine when it is no longer possible to distinguish between the polygon and the curve. Nevertheless, the two shapes will be mathematically different objects.