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eroshea Group Title

A regular hexagon A has the midpoints of its edges joined to form a smaller hexagon B. This process is repeated by joining the midpoints of the edges of the hexagon B to get a third hexagon C. What is the ratio of the area of hexagon C to the area of hexagon A?

  • 2 years ago
  • 2 years ago

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  1. hartnn Group Title
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    Each smaller hexagon formed will have side length equal to 0.866(half times square root of 3)times the length of its previous hexagon

    • 2 years ago
  2. eroshea Group Title
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    how did you get that?

    • 2 years ago
  3. hartnn Group Title
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    |dw:1350381371686:dw|

    • 2 years ago
  4. hartnn Group Title
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    sorry for bad drawing, but could u get the side of smaller hex from that ?

    • 2 years ago
  5. eroshea Group Title
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    it's fine.. i'll analyze it for a while

    • 2 years ago
  6. hartnn Group Title
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    |dw:1350381577682:dw|

    • 2 years ago
  7. eroshea Group Title
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    what was that d/2 ??

    • 2 years ago
  8. hartnn Group Title
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    yes, d/2 or u asked , why was that d/2 ?

    • 2 years ago
  9. eroshea Group Title
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    i meas WHAT is that d/2? where did you get it? sorry but i find solid mensuration and geometry hard ..

    • 2 years ago
  10. hartnn Group Title
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    d is the side of smaller hexagon , so the length i have marked here will be d/2 |dw:1350381918942:dw|

    • 2 years ago
  11. eroshea Group Title
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    ahh.. got it.. i was confused from that equation :D

    • 2 years ago
  12. hartnn Group Title
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    so u will have ratio of sides, know how to find ratio of areas ?

    • 2 years ago
  13. eroshea Group Title
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    no, i don't

    • 2 years ago
  14. hartnn Group Title
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    (ratio of sides)^2 = ratio of areas ALWAYS.

    • 2 years ago
  15. eroshea Group Title
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    owh.. so like the equation on how i got the corresponding sides of the 2 triangles? ok.. got it.. i'll just now solve for the sides of the hexagon C

    • 2 years ago
  16. hartnn Group Title
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    yes, find the ratio of sides of hex A and hex C.

    • 2 years ago
  17. eroshea Group Title
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    9/16 ?? ahm.. is it??

    • 2 years ago
  18. hartnn Group Title
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    yes!

    • 2 years ago
  19. hartnn Group Title
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    9/16 is ratio of areas

    • 2 years ago
  20. eroshea Group Title
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    i thought i was wrong :D that problem is complicated for me. thanks for the help man! :))

    • 2 years ago
  21. hartnn Group Title
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    welcome ^_^

    • 2 years ago
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