Question 1173192
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The area of an equilateral triangle with side length x is {{{A = (sqrt(3)/4)*x^2}}}


For equilateral triangle ABC, we have x = 4 as the side length. The area of triangle ABC is 
{{{A = (sqrt(3)/4)*x^2}}}


{{{A = (sqrt(3)/4)*4^2}}}


{{{A = sqrt(3)*(1/4)*16}}}


{{{A = sqrt(3)*4}}}


{{{A = 4*sqrt(3)}}}


The regular hexagram is composed of a regular hexagon with equilateral triangles attached to each of the six edges of the hexagon.
We can break up the regular hexagon into 6 equilateral triangles that are all congruent to one another. These 6 additional triangles are identical to the triangles that line the outside of the hexagon.


In short: we have 6+6 = 12 equilateral triangles that are identical.


Because we have 12 identical triangles, each with area {{{A = 4*sqrt(3)}}}, this means the total area of the regular hexagram is {{{12A = 12*4*sqrt(3) = 48*sqrt(3)}}}


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Answer: <font color=red>A) 48 √ 3</font>
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