No. of equilateral triangles required to completely fill a bigger equilateral triangle

Question

$\triangle ABC$ is equilateral with side length=2.1cm

Smaller equilateral triangles with side length=1cm are placed over $\triangle ABC$ so that it is fully covered. Find the minimum number of such small triangles.

I am not getting it. How is it possible to completely fill with such dimensions?

@ Hagen von Eitzen that might be the case. Since I am unable to get it without overlapping. — Rudstar, May 06 '14 at 14:33

score 3 · Accepted Answer · answered May 06 '14 at 15:09

3

This is not answer to the question.

I just post a rough sketch showing a way of how the 6 equilateral triangles can be arranged to cover the original. enter image description here

answered May 06 '14 at 15:09

Mick

17,141

score 2 · Answer 2 · answered May 06 '14 at 14:36

Six triangle suffice (three in the corners and three in the middle of the sides). It is not possible with less than six triangles: Let $D$ be the midpoint of $AB$, $E$ the midpoint of $BC$, $F$ the midpoint of $CA$. Then the distance between any two of the points $A,B,C,D,E,F$ is $\ge1.05>1$, hence no two of them can be covered by the same side-1-triangle.

No. of equilateral triangles required to completely fill a bigger equilateral triangle

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