fencing problem

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I have been given the fencing problem course work by my teacher. In this piece of course work I will be using ict (excel to help me draw graphs and word) and be drawing graphs to explain my statistics. This piece of course is about:

A farmer as exactly 1000 meter of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 100m so it could be anything else with a perimeter (or circumference) of 1000m. She wishes to fence off the plot of land, which contains the maximum area.

 

The propose of this course is to work out all the maximum area for 1000 meter fence by drawing and calculating with 2D different shapes.

I resolve my problem by drawing triangles, rectangles, squares, circle and polygons, to study which shape could attain the maximum area of 1000 meter. Firstly I will be drawing 4 triangles with the perimeter of 1000 meter. Secondly I will draw the quadratral family for example squares and rectangles. Next I’ll draw polygons up to 5sides to 10sides, and I will be calculating the nth side using the nth formula. To end with I will calculate the area of the circle.

I predict that the circle will get the maximum area because its area is immeasurable and predict that area of a polygon will rise depending of the number of sides.

 

                                             

Triangles

I will begin my investigation by drawing 4 triangles to find the maximum area with the perimeter of 1000m²

From my table I am able to see which shape has the maximum area, and the shape with the maximum area is the regular shape which is an equilateral triangle. And the graph will back predicti

Calculating the maximum area of

Triangles with the perimeter of

1000m²

333.3²                           333.3²                                   400²                                    400²

                    H

             

 

                333.3² = 166.7²                                                                200² = 100²  

                   2                                                                    2

333.3²-166.7²                                                                       400² -100²  

H² = 111088.89-27788.89                                                  H² = 160000-10000

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 83300 =288.6                                                                       150000 = 387.2

Area= 333.3×2886 = 48095.19m²                                        Area= 200×3872= 38720m²

                  2                                                                      2

300²               ...

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