# 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?

1. John Rey Jimenez. Negros Occidental High School

2. Arsh Singh. yourmathguru.com

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

12. Carlo Jay Vizcarra. Pamantasan ng Lungsod ng Maynila

### 13 Responses

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

(648√2)/11

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

108√2 cm^2

3. JM Maninang says:

John Michael Maninang
UST

162 sqrt (3)

4. JM Maninang says:

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

5. JM Maninang says:

72 sqrt(3)?

6. JM Maninang says:

Last try. :)) 216 sqrt(3)

7. Jhay Dela Cruz says:

216sq.root of 3

PUP -Taguig

8. 374.1229744348773 cm^2

9. Shamik Banerjee says:

216*sqrt(3) = 374.1229744 square cm

10. Shamik Banerjee says:

216*sqrt(3) = 374.1229744 square cm

Kendriya Vidyalaya Cossipore

11. Anuraag says:

54sqrt(3)

12. Carlo Jay Vizcarra says:

216sqrt(3) – PLM

13. 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.