Respuesta :
7.2 percent of the area of the original hexagon was removed
The area of hexagon is the region that lies within the sides of the hexagon. A hexagon is a two-dimensional shape that has 6 sides, 6 angles, and, 9 diagonals, and the sum of its interior angles is 720°
Area of the hexagon = (3√3 s2)/2, where 's' is the length of the side of the hexagon.
Her, We have
[tex]\(1-2s=s\sqrt3, 1=2s+s\sqrt3, 1=s(2+\sqrt3), s=\frac{1}{2+\sqrt3}\)[/tex]
Rationalize the denominator to get [tex]\(s=2-\sqrt3\)[/tex]
The area of the hexagon is [tex]\(\frac{3\sqrt3}{2}\)[/tex] and the dodecagon is [tex]\(\frac{3s^2\sqrt3}{2}\).[/tex]
The deleted area is [tex]\(s^2=0.072=7.2%\)[/tex] percent
Formula used:
Area = (3√3 s2)/2
Learn more about Polygon:
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