Question

A regular hexagon is truncated to form a regular dodecagon (12-gon) by removing identical isosceles triangles from its six corners. What percent of the area of the original hexagon was removed

Answer 1

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

$\(1-2s=s\sqrt3, 1=2s+s\sqrt3, 1=s(2+\sqrt3), s=\frac{1}{2+\sqrt3}\)$

Rationalize the denominator to get $\(s=2-\sqrt3\)$

The area of the hexagon is  $\(\frac{3\sqrt3}{2}\)$  and the dodecagon is $\(\frac{3s^2\sqrt3}{2}\).$

The deleted area is $\(s^2=0.072=7.2%\)$ percent

Formula used:

Area = (3√3 s2)/2

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