20.3 cm 2
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Another opinion:
I've never done one of these before, but I tried this one,
and for my answer, I got 140.5 cm2.
Yes, a square with sides measuring ten centimeters can completely fit inside a regular hexagon with sides also measuring ten centimeters. The hexagon's interior angles and the distances from the center to the vertices allow for a square to be inscribed within it, as the square's diagonal is shorter than the hexagon's width at its widest points. Specifically, the diagonal of the square is approximately 14.14 centimeters, which is less than the distance between opposite sides of the hexagon. Thus, the square can be accommodated within the hexagon without any overlap.
Put one angle of each triangle at the center of the hexagon.
It is at the intersection of the hexagon's lines of symmetry, i.e. the middle! It is the midpoint of any diameter.
It probably is a regular hexagon. Take the Apothem (The distance from the center to a side) and multiply by one half and by the perimeter. if the sum of interior angles of a polygon is 120 then (n-2)180=120==>n=8/3 which is impossible
if r = perpendicular distance center of hexagon to a side, and r^2 = r squared, then AREA = 6x r^2 x tan 30 degrees = 3.464 r^2 or if R = distance center of hexagon to a corner, AREA = 3 R^2 sin 60 = 2.598 R^2
Put one angle of each triangle at the center of the hexagon.
It is at the intersection of the hexagon's lines of symmetry, i.e. the middle! It is the midpoint of any diameter.
From each vertex to its opposite vertex. These will be centered on a shared point at the center of the hexagon. Each complete line will be a line of symmetry for the hexagon.
It probably is a regular hexagon. Take the Apothem (The distance from the center to a side) and multiply by one half and by the perimeter. if the sum of interior angles of a polygon is 120 then (n-2)180=120==>n=8/3 which is impossible
3.55
if r = perpendicular distance center of hexagon to a side, and r^2 = r squared, then AREA = 6x r^2 x tan 30 degrees = 3.464 r^2 or if R = distance center of hexagon to a corner, AREA = 3 R^2 sin 60 = 2.598 R^2
No, it is the distance from the center of the polygon to the centre of one of its sides.
A Apothem
A regular hexagon can be carried onto itself by rotations of 60 degrees, 120 degrees, 180 degrees, 240 degrees, and 300 degrees around its center. These rotations correspond to the multiples of 60 degrees, which are the angles formed by the vertices of the hexagon. Additionally, a 0-degree rotation (no rotation) also carries the hexagon onto itself.
That is called the apothem. The definition is: An Apothem is the distance from the center of a regular polygon to the midpoint of a side
P=perimeter s=sides h=altitude (distance from the center to a side at a right angle) A=1/2aP or A=1/2(6s x a) Edit - If the hexagon is regular, the area can be found by this formula: 3s^2 * 3^(1/2) / 2 Where s=side length of the hexagon and in this case squared and 3^(1/2)=square root of 3
Apothem