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Firstly I will investigate rectangles to find the maximum area of that shape. The following table shows the formulas I used to obtain the results for the different rectangles. Length (L) Width (500-L) Area L(500-L) (m) (m) (m²) 10 =(500-A3) =A3*B3 20 =(500-A4) =A4*B4 30 =(500-A5) =A5*B5 40 =(500-A6) =A6*B6 50 =(500-A7) =A7*B7 100 =(500-A8) =A8*B8 150 =(500-A9) =A9*A9 200 =(500-A10) =A10*B10 250 =(500-A11) =A11*B11 Here are my results: Length (L) Width (500-L) Area L(500-L) (m) (m) (m²) 10 490 4900 20 480 9600 30 470 14100 40 460 18400 50 450 22500 100 400 40000 150 350 52500 200 300 60000 250 250 62500 From these results we can see that the largest area belongs to the rectangle with the dimensions of 250x250. Therefore the rectangle with the largest area is actually a square. 250m 250m x 250m = 62,500m² 250m I will now investigate triangles; I will start with an equilateral triangle. To find out the length for each side, you need to divide 1000 (the perimeter) by 3 (number of sides). 1000 = 333.3m. 3 I need to keep in mind that the answer is actually 333.3 recurring. 333.3m (a) To work out the area I need to find the height of the triangle. To do this I will split...

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