Freehand Geometry: (December 7 – December 14, 2013)


Sum of Infinite Area

A regular hexagon has a side 6 cm. A smaller hexagon was drawn by connecting the midpoints of the side of the larger hexagon. The process is repeated continuously. What is the sum of their areas?


Comment your answer below. Note: I am the only one who can see your comments. You are only allowed to comment your answer once. Comments will be revealed next week December 14,2013(Philippines Time).You can also send your answer to  Please don’t forget to include the name of your school.Names of those who commented the correct answer will be posted in this page immediately after the answer has been reviewed. Happy Solving!


Correct answer were submitted by:

1. John Rey Jimenez. Negros Occidental High School

2. Arsh Singh.

3. Jomari Tan. DLSU

4. Marlon Chris Malicsi. UST

5. JM Maninang. UST

6. Jhay Dela Cruz. PUP -Taguig

7. Nabeel Kabeer Leo XIII  (school/affiliation please)

8. Muthu Krishna. Kle college , Bengaluru

9. Fo Chik Yong.  (school/affiliation please)

10. Shamik Banerjee. Kendriya Vidyalaya Cossipore

11. Russelle Guadalupe. UP Diliman

12. Carlo Jay Vizcarra. Pamantasan ng Lungsod ng Maynila



Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

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13 Responses

  1. Gio Alfred Gloria. Cauayan City National High School says:


  2. Gio Alfred Gloria. Cauayan City National High School says:

    108√2 cm^2

  3. JM Maninang says:

    John Michael Maninang

    162 sqrt (3)

  4. JM Maninang says:

    Oppps. Try again. :)) 81 sqrt(3)

  5. JM Maninang says:

    Last try. :)) 216 sqrt(3)

  6. Jhay Dela Cruz says:

    216sq.root of 3

    PUP -Taguig

  7. 374.1229744348773 cm^2

  8. Shamik Banerjee says:

    216*sqrt(3) = 374.1229744 square cm

  9. Shamik Banerjee says:

    216*sqrt(3) = 374.1229744 square cm

    Kendriya Vidyalaya Cossipore

  10. Anuraag says:


  11. Carlo Jay Vizcarra says:

    216sqrt(3) – PLM

  12. kryptonj123 says:

    No more comments. Next problem will be publish tonight.

    the correct answer is $latex 216\sqrt{3} cm^2$

    Solution will be presented later.

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