SOLUTION: In the regular hexagram shown at the bottom, Line AB=4 cm. The area of the hexagram, in cm^2 is: A) 48 √ 3 B) 24 √ 3 C) 18 √ 3 D) 20 √ 3 E)22 √ 3 https://ibb.co

Question 1173192: In the regular hexagram shown at the bottom, Line AB=4 cm. The area of the hexagram, in cm^2 is:
A) 48 √ 3
B) 24 √ 3
C) 18 √ 3
D) 20 √ 3
E)22 √ 3
https://ibb.co/xfhPGWG
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The area of an equilateral triangle with side length x is

For equilateral triangle ABC, we have x = 4 as the side length. The area of triangle ABC is

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 , this means the total area of the regular hexagram is

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Answer: A) 48 √ 3

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