In the regular hexagram shown to the right, AB= 4 cm. Find the area.

[randy.lahey]

In the regular hexagram shown to the right, AB= 4 cm. The area of the hexagram, in cm^2, is

 

[Zormuche]

Hello
the hexagon can be divided into 6 similar equilateral triangles, which have the same size and area than the ABC triangle

so the area of the whole hexagram is 12 triangles

Using pythagoras theorem in ABC, you can see the height is 2sqrt(3), so the area is 4 * 2sqrt(3) / 2 = 4sqrt(3)

So the total area of the hexagram is 12 * 4sqrt(3) = 48sqrt(3)