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Further Mathematics Support Programme

Discover the number of different length diagonals in a regular dodecagon and learn how to calculate their lengths. Gain surds skills by expanding and simplifying expressions involving square roots.

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Further Mathematics Support Programme

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  1. Further Mathematics Support Programme

  2. Diagonals in a Dodecagon Let Maths take you Further…

  3. Diagonals in a dodecagon How many different length diagonals are there in a regular dodecagon?

  4. Diagonals in a dodecagon • The side length AB is 2 units. • All shapes shown are regular. • The diagonal AD is a line of symmetry for the squares and triangles it dissects. • How could you calculate the lengths: • AC • AD • AE • AF • AG?

  5. Surds skills • Expanding the expression: • Hence, to find the square root of an expression involving surds, it is sometimes possible to manipulate the expression in order to obtain something in the form of: • This can then be factorised to: • Finding the square root of this gives:

  6. Surds skills This has to be ‘2’ Simplify Try the method to simplify the following expressions: a) b) c)

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