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MathNet 2012 Question 62

Math Olympiad Vault · MathNet 2012

Question 62

The figure shows a regular dodecagon divided into six equilateral triangles, six squares, and a regular hexagon, all with the same side length.

Question illustration

a) If each triangle has area $1\,\mathrm{cm}^2$, what is the hexagon's area?

b) The following figure was obtained by removing twelve equilateral triangles from a regular dodecagon of side $1\,\mathrm{cm}$. What is its area?

Question illustration

c) The following figure was obtained by removing two regular hexagons from a regular dodecagon of side $1\,\mathrm{cm}$. What is its area?

Question illustration