# 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 techiemathteacher@gmail.com. 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. 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

11. Russelle Guadalupe. UP Diliman

12. Carlo Jay Vizcarra. Pamantasan ng Lungsod ng Maynila

### Dan

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(648√2)/11

108√2 cm^2

John Michael Maninang

UST

162 sqrt (3)

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

72 sqrt(3)?

Last try. :)) 216 sqrt(3)

216sq.root of 3

PUP -Taguig

374.1229744348773 cm^2

216*sqrt(3) = 374.1229744 square cm

216*sqrt(3) = 374.1229744 square cm

Kendriya Vidyalaya Cossipore

54sqrt(3)

216sqrt(3) – PLM

No more comments. Next problem will be publish tonight.

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

Solution will be presented later.