The fencing problem - maths

So far in my investigation I have found the largest areas for rectangle and triangles. From the results of both of them I have found that the ones with the largest area are regular shapes, such as a square or equilateral triangle. So I believe from now on in my investigation, I am only going to investigate regular shapes.

   I am now going to move on and investigate many other regular polygons, such as pentagons and hexagons.

Polygons

The graph shows that, as the number of sides increases, the area of the shape increases also. This theory, shown and proven by the graph, can be applied to as many sides as possible until it reaches the point of a true circle. A circle has an infinite number of sides, therefore making the area as big as it could possibly be. The graph at this point wouldn't ascend any further, it would simply flatten out to show the lack of increase.

Therefore, in conclusion, I have found in this piece of coursework, that the more sides the fence has the more its area will increase. Therefore I believe that if I carried on this pattern that the shape with the biggest area would be a circle as it has an infinite amount of sides, so its area couldn’t get any bigger.