can u help me with thisquestion?

Question

you are provided a regular hexagon take 7 points inside and show that the distance between two of them is less than 2 units(given area of hexagon is 6root3 units.

also does any one know wat php is in plane geometry

Answer 1

Connect the center of the hexagon to each of the vertex's, forming 6 equalateral triangles. By placing 7 points in this hexagon, at least two must be in the same triangle by the pigeon hole principle. You can encompass one of these triangles with a circle with radius of 6root3, so the claim you are after is true.

Answer 2

The area of a hexagon is (3/2)(√3)(s^2) where s is the side length. So if this is 6√3, then
(3/2)√3(s^2) = 6√3
(3/2)(s^2) = 6
s^2 = 6*2/3
s = √(12/3) = 2

If you pick the points that are on each vertext of the hexagon plus the center point, these seven points are 2 units or more away from each other. So for any seven points inside of the hexagon, you can't have all of the distances all be more than 2 units.

Answer 3

formula for area of hexagon is

6 individual equilateral triangles make up the hexagon

If we put seven points, then at least two of them must be in the same triangle.

We have to figure out the dimensions of the triangle, to show they are within two units

If the total area is 6sqrt3, then each equilateral triangle has an area of sqrt3
The formula for an equilateral triangle is
A = sqrt3 / 4 * (side)^2
sqrt3 = sqrt3 / 4 * s^2
s^2 = 4
s = 2

Each side of the equilateral triangle is length 2, so two points must be within this distance.

good luck to you!

=]

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Answer 4

Plane geometry deals with two-dimensional figures only, while solid geometry has to do with three or more dimensions (there are geometries that deal with more than three), and special geometries that deal with solids that have curves.