## eroshea 3 years ago 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?

1. hartnn

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. eroshea

how did you get that?

3. hartnn

|dw:1350381371686:dw|

4. hartnn

sorry for bad drawing, but could u get the side of smaller hex from that ?

5. eroshea

it's fine.. i'll analyze it for a while

6. hartnn

|dw:1350381577682:dw|

7. eroshea

what was that d/2 ??

8. hartnn

yes, d/2 or u asked , why was that d/2 ?

9. eroshea

i meas WHAT is that d/2? where did you get it? sorry but i find solid mensuration and geometry hard ..

10. hartnn

d is the side of smaller hexagon , so the length i have marked here will be d/2 |dw:1350381918942:dw|

11. eroshea

ahh.. got it.. i was confused from that equation :D

12. hartnn

so u will have ratio of sides, know how to find ratio of areas ?

13. eroshea

no, i don't

14. hartnn

(ratio of sides)^2 = ratio of areas ALWAYS.

15. eroshea

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

16. hartnn

yes, find the ratio of sides of hex A and hex C.

17. eroshea

9/16 ?? ahm.. is it??

18. hartnn

yes!

19. hartnn

9/16 is ratio of areas

20. eroshea

i thought i was wrong :D that problem is complicated for me. thanks for the help man! :))

21. hartnn

welcome ^_^