Question 1165480
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Note the statement of the problem should specify a REGULAR hexagon; without that, the problem is not defined well enough to get an answer.<br>
Area of square which is inscribed in the circle: 72<br>
Side of square: {{{sqrt(72) = 6*sqrt(2)}}}<br>
Diagonal of square = diameter of circle: {{{(6*sqrt(2))*sqrt(2) = 12}}}<br>
The circle is inscribed in the hexagon; the diameter of the circle is the distance from the middle of one side of the hexagon to the middle of the opposite side.<br>
View the hexagon as being composed of 6 equilateral triangles.  The radius of the circle, length 12/2=6, is the long leg of a 30-60-90 right triangle in which the hypotenuse is the length of one side of one of those equilateral triangles.<br>
Side length of hexagon = side length of one of the equilateral triangles = {{{6*(2/sqrt(3)) = 12/sqrt(3) = 4*sqrt(3)}}}<br>
Area of hexagon = area of 6 equilateral triangles = {{{6((s^2*sqrt(3))/4) = 6((48sqrt(3))/4) = 72sqrt(3)}}} = 124.71 to 2 decimal places.<br>
ANSWER: a. 124.71 sq cm<br>