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Isoperimetric Quotients Isoperimetric Quotients of plane shapes are calculated using the formula: I.Q. = 4? x Area of shape (Perimeter of shape)² I am going to investigate isoperimetric quotients of plane shapes and interpret my findings. Firstly, I am going to look at flat shapes. Using the formula, I will calculate the isoperimetric quotients of the shapes. Starting with the smallest 2D shape- a triangle- I will calculate the I.Q s of right-angled triangles. I will also do this with isosceles and equilateral triangles. I will move on to quadrilaterals and look at the I.Q s. Maybe there will be something about the results that will help me with further plane shapes; pentagon, hexagon, heptagon, nonagon, decagon and possibly a circle. With comparison, the results might show something about the shapes, such as a pattern. Triangles I am now going to study right-angled triangles. Right-angled triangles I will first look at the 3, 4, 5 right-angled triangles...

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