Answer:
Exact area = [tex]\frac{3}{2}\sqrt{3}[/tex] square cm
Approximate area = 2.598 square cm
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Work Shown:
s = side length of equilateral triangle = 1 cm
A = area of equilateral triangle with side length 's'
[tex]A = \frac{\sqrt{3}}{4}*s^2[/tex]
[tex]A = \frac{\sqrt{3}}{4}*1^2[/tex]
[tex]A = \frac{\sqrt{3}}{4}[/tex]
This is just one of the 6 equilateral triangles (see diagram below)
Multiply by 6 to get the area of all 6 equilateral triangles, or the entire hexagonal area
[tex]6*A = 6*\frac{\sqrt{3}}{4}[/tex]
[tex]6A = \frac{3\sqrt{3}}{2}[/tex]
[tex]6A \approx 2.598[/tex]
