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Investigate Isoperimetric Quotients of plane shapes and interpret your findings.
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Maths Coursework-Isoperimetric Quotients Introduction Isoperimetric quotients of plane shapes can be calculated using the formula: I.Q = 4? x Area of shape (Perimeter of shape) 2 Investigate Isoperimetric Quotients of plane shapes and interpret your findings. Squares Area = 10x10 =100 cm2 Perimeter = 10x4 = 40cm 10cm 10cm I.Q= 4? x Area of shape (Perimeter of shape)2 = 4? x 100 402 = 0.7853 Area = 100 x100 = 10000cm2 Perimeter = 100x 4 = 400cm I.Q= 4? x Area of shape (Perimeter of shape)2 = 4? x 10 000 4002 = 0.7853 Formula I can algebraically prove that the Isoperimetric quotient of a square will always = 0.7853 thus: I.Q= 4? x l2 (4l)2 = 4? x l2 16 l2 = 4? 16 = ? 4 = 0.7853 This proves that for any given square the Isoperimetric Quotient will be the same at 0.7853. Rectangles Area = 10 x20 =...
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