Regular dodecagon ABCDEFGHIJKL with side length 1 is drawn. Segments AF, BG, and CH are then drawn.
A tiny little triangle is formed from the intersections of these segments. Find the area of this triangle.
It is quite difficult to reproduce here the path to solve this puzzle.
what I did is work on ABG. With big designs and easy math you can get all the principal measures (lenght and angles)
After that one should note that the inferior extreme of the base of the tiny triangle (the bigger dimension) is aligned with OE. This give a necessary angle.
Then you see that the tiny triangle is an isosceles 30° triangle with a base b=tan(15)
The area is then:
A=b*h/2= tan(15)*[1/4*tan(15)*tan(30)]=0,01036
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Posted by armando
on 2019-03-16 12:38:21 |
Solution
