Equible Shapes

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Jamie Watson 11HC                                            Equable Shapes Coursework

Maths Coursework - Equable Shapes

A 2 dimensional equable shape is a shape whose area and perimeter are equal.

Example:

                                     Area         =  4 * 4             = 16

4cm                              Perimeter =  4 + 4 + 4+ 4 = 16

                   4cm

The formula for all two dimensional equable shapes must be:

               Perimeter = Area

I tried to work out the formula of any regular polygon. I realised that all regular polygons could be broken down into isoceles triangles:

Using only the side, length, x, it is possible to dicover the height of each of these triangles. Using the height I can then calculate the area of each triangle. By multiplying the number of triangles, of which there are the same amount as of sides,  by the area of each, I can discover the total area of the shape.

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        I can then calculate the perimeter by multiplying the side length, x, but the number of sides, n.

        

        

I will use a hexagon as an example:

x is the side length of the hexagon. It is also the base of the triangles the hexagon is made up of:

As a hexagon has six sides, I can work out the angles that are ...

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