The Fencing Problem - Mathematics :: Math Coursework Mathematics

The Fencing Problem Introduction ============ I have been given 1000 meters of fencing and my aim is to find out the maximum area inside. ====================================================================== Prediction ---------- I would predict that the more sides the shape has, then possibly the bigger the area it will have, although I have nothing to base this on, it will be what I am about to investigate. Shapes: I am going to start with the rectangle, I think this is a good starting block because I am able to vary the widths and lengths to see which has the bigger area. If I discover that the rectangles with equal sides i.e. square bring me the best result, then I will try to direct my investigation into furthering that particular theory. Rectangles ---------- [IMAGE] Area = 40 000 m2 ================ [IMAGE] Area = 60 000 m2 [IMAGE] Area = 62 500 m2 It appears that the square shape has a bigger area, I would possibly say that this is because the square has two bigger numbers, which are multiplied together to give a greater number than when a big number is multiplied with a smaller number. However, I cannot take this for granted and I think using one more shape will be useful in order to back up my theory. [IMAGE] Area = 52 500m This proves my theory regarding squares and I shall now put my results into a graph to show what I have found. Length (m) Width (m) Area (m) 400 100 40 000 300 200 60 000 250 250 62 500 150 350 52 500 I will now further my investigation by looking at shapes of a different nature: [IMAGE] Regular Pentagon ---------------- The regular pentagon has 5 sides, and as we get 1000m of fencing, this means each side will be 200m (1000Â ¸5=200).