# Is a regular hexagon an equilateral?

## Is a regular hexagon an equilateral?

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.

Is a hexagon equilateral or equiangular?

### Can a hexagon be equilateral but not equiangular?

Answer Expert Verified. Yes, it is possible to have a hexagon which is equiangular and not equilateral. The six interior angles of a hexagon measures 120 degrees each thus it is equiangular. If the two parallel sides of the hexagon are longer than the other sides then the hexagon is not equilateral anymore.

How do you prove a hexagon is equilateral?

The angle at the center of the hexagon is 360° which is being divided into 6 equal parts. Thus, the value of each angle at the center is equal to 60°. Hence, we see that all three angles of the 6 triangles formed in the given hexagon are equal to 60°. This proves that there are 6 equilateral triangles.

#### Does a hexagon have 6 equilateral triangles?

A hexagon is made up of 6 congruent equilateral triangles. Each equilateral triangle has a length of 8 units.

What is special about a hexagon?

But what makes hexagons so special? A hexagon is the shape that best fills a plane with equal size units and leaves no wasted space. Hexagonal packing also minimizes the perimeter for a given area because of its 120-degree angles.

## Is any shape with 6 sides a hexagon?

A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides…

Is a rhombus an equilateral?

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length….

Rhombus
Dual polygon rectangle
Properties convex, isotoxal

### Is a rhombus equiangular and equilateral?

A rhombus has all sides which are always equal to each other but the interior angles of a rhombus are not equal. The opposite angles are equal to each other but the adjacent angles are not equal to each other. Thus, a rhombus is equilateral but not equiangular.

How do you prove a hexagon?

For any polygon, the sum of the interior angles is S=(n-2)•180°, where n is the number of sides of the polygon. In a hexagon, n=6, so the sum of the interior angles in a hexagon is (6-2)•180°=4•180°=720°. And since all the interior angles of a regular hexagon are equal, each one measures 720°/6=120°.

#### Which is a hexagon that is both equiangular and equilateral?

Is a hexagon equilateral? A regular hexagon is defined as a hexagon that is both equilateral and equiangular. From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles.

Is the length of a regular hexagon always equal?

The length of each side of a regular hexagon is equal. It is a symmetrical shape since each side is of equal length. Opposite sides of a regular hexagon will always be parallel to each other. A regular hexagon can be split into 6 equilateral triangles.

## Can a hexagon be partitioned into six equilateral triangles?

From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles. Click to see full answer. Besides, is a hexagon made of equilateral triangles?

What kind of symmetry does a regular hexagon have?

A regular hexagon has six rotational symmetries ( rotational symmetry of order six) and six reflection symmetries ( six lines of symmetry ), making up the dihedral group D 6. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side.