SOLUTION: Find the area of the largest circle that can be inscribed in a hexagon of side “h”. A.2.356 h2 B.2.441 h2 C.3.146 h2 D.1.786 h2

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Find the area of the largest circle that can be inscribed in a hexagon of side “h”. A.2.356 h2 B.2.441 h2 C.3.146 h2 D.1.786 h2      Log On

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Question 1153295: Find the area of the largest circle that can be inscribed in a hexagon of side “h”.
A.2.356 h2
B.2.441 h2
C.3.146 h2
D.1.786 h2
Answer by MathLover1(20850) About Me  (Show Source):
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From the figure, it is clear that, we can divide the regular hexagon into+6+identical equilateral triangles.
We take one triangle+OAB, with O as the center of the hexagon or circle, & AB as one side of the hexagon.
Let M be mid-point of AB, OM would be the perpendicular bisector of AB, angle AOM+=+30°
Then in right angled triangle OAM,side a (in your case is h)
tan%28x%29+=+tan%2830%29+=+1%2Fsqrt%283%29
So,
h%2F2r+=+1%2Fsqrt%283%29
Therefore,
r+=+%28h%2Asqrt%283%29%29%2F2
Area of circle is:

A+=pi%2Ar%5E2
A+=pi%2A%28%28h%2Asqrt%283%29%29%2F2%29%5E2
A+=%283%2Api%2F4%29h%5E2
A+=2.356.h%5E2

answer: A.2.356h%5E2