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In my investigation I am going to work on different shapes with a perimeter of 1000 meters. I will try to find the shape with the largest area.
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Math Coursework In my investigation I am going to work on different shapes with a perimeter of 1000 meters. I will try to find the shape with the largest area. First I have decided to try the simplest type of shapes, which are triangles (only 3 sides). 3 Types of triangles: 1. Isosceles: This triangle has only two sides equal while the third is not. B A C M In triangle ABC: AB = BC, BM is perpendicular to AC and divides into two equal halves (AM & CM). If AB = 400m , BC = 400m , AC = 100m Therefore AM = MC = 250m By Pythagoras theorem: BM2 = BC2 - MC2 BM2 = 4002 - 1002 BM2 = 160000 - 10000 = 150000 BM = 387.2983346m Area of triangle BMC = 1/2 x base x perpendicular height = 1/2 x 100 x 387.2983346 = 19364.91673 Area of triangle ABC = 19364.91673 x 2 = 38729.83346m2 Formula for any isosceles triangle: Base =...
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