1. Draw a regular hexagon then draw the six "alternate" vertices.

(Skip one vertex - 1 to 3, 2 to 4 etc). If the area of the original hexagon is 6,

what is the area of the internal hexagon that is formed?

So I don't have to type "sqrt(3)"!):

u = sqrt(3)

v = 1/u (ratio radii outer:inner)

R = outer radius

Pentagon area: 3u(R^2) / 2

Given: area = 6 ; soooooo:

3u(R^2) / 2 = 6

R = sqrt(4 / u) : ~1.5196....

r = inner radius

r = R * v : ~.8773....

area = 3u(r^2)/2

area = (drum rolls!) 2 exactement.

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