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Table of Contents INTRODUCTION 3 RIGHT ANGLE TRIANGLES 3 PAIR ONE. 3 PAIR TWO 4 RESULTS 5 ISOSCELES TRIANGLES 5 PAIR ONE 5 PAIR TWO 6 RESULTS 7 EQUILATERAL TRIANGLES 7 RESULTS 8 FOUR SIDED SHAPES 8 SQUARES 8 Results 9 RECTANGLES 9 Results 10 IRREGULAR FOUR SIDED SHAPES 11 Results 11 FIVE-SIDED-SHAPES 12 PENTAGONS 12 Results 13 IRREGULAR PENTAGONS 14 Results 15 SIX-SIDED SHAPES 15 HEXAGONS 15 Results 16 IRREGULAR HEXAGONS 16 Results 17 GENERAL FORMULA 17 HEPTAGON 18 OCTAGON 18 ALL REGULAR SHAPES 19 CIRCLE 20 FINAL CONCLUSION 21 Isoperimetric Quotients Introduction I am going to explore the different IQs for different shapes and try to find how the IQ relates to the shape. The formula for the IQ of a shape is IQ = 4?xArea / Perimeter^2 I will compare similar shapes, look at regular and irregular polygons and try to find patterns. Right Angle Triangles I will start with Right Angle Triangles; I will look at four triangles with two pairs of similar triangles. Pair One. The two triangles I looked at had the same area but different IQs. This shows that IQs are not directly related to the area of the shape. In my next pair I will look at similar shaped triangles. Pair Two The two triangles had identical IQs even though their area and perimeters...

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