Basic geometry question regarding hexagons.

  • Thread starter Gazarai
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In summary, the conversation is about finding the longest diameter of an irregular hexagon with 3 different sets of sides. The sides are equal in length to the opposite side and different from the sides beside it. The question is whether the largest possible diameter is half the perimeter or if there is more information needed, such as the angles, to create a formula with 3 variables representing the sets of sides.
  • #1
Gazarai
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I'm trying to figure out how to find the longest diameter of any irregular hexagon with 3 different sets of sides. Each side is the same in length as the side opposite it, and different in length to both sides beside it. Any help?
 
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  • #2
Err, I should note that I know *how* to find it, and that what I can't seem to figure out is how to put it into a formula, with 3 variables representing the 3 sets of sides.
 
  • #3
Is the largest possible diameter not half the perimeter, using a degenerate hexagon?

Or is there something you haven't told us, say, regarding the angles?
 

1. What is a hexagon?

A hexagon is a two-dimensional geometric shape with six sides and six angles. It is a polygon, which means it is a closed shape made up of straight lines.

2. How do you find the perimeter of a hexagon?

To find the perimeter of a hexagon, you add together the lengths of all six sides. If all six sides are the same length, you can simply multiply that length by six.

3. What is the formula for finding the area of a hexagon?

The formula for finding the area of a hexagon is A = (3√3/2) x s², where s is the length of one side. This formula applies to regular hexagons, where all six sides are the same length. For irregular hexagons, you would need to break the shape into smaller, more manageable shapes and use their respective area formulas.

4. Can you have a concave hexagon?

Yes, it is possible to have a concave hexagon. A concave hexagon is a hexagon with at least one interior angle greater than 180 degrees. This means that the sides of the hexagon "cave in" instead of being straight.

5. How many diagonals does a hexagon have?

A hexagon has nine diagonals. A diagonal is a line segment that connects two non-adjacent vertices (corners) of a polygon. In a hexagon, each vertex has two diagonals extending from it, except for the two vertices at the ends of the longer side, which have three diagonals each.

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