A hexagon is a closeup of the door 2D form that is consisted of of straight lines. That is a two-dimensional shape with 6 sides, 6 vertices, and also six edges. The name is split into hex, which means six, and gonia, which way corners.

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 1 Hexagon Definition 2 Types of Hexagon 3 Properties of a Hexagon 4 Hexagon Formulas 5 FAQs ~ above Hexagon

Hexagon is a two-dimensional geometrical form that is make of 6 sides, having actually the exact same or different dimensions that length. Part real-life examples of the hexagon are a hexagonal floor tile, pencil, clock, a honeycomb, etc. A hexagon is one of two people regular(with 6 same side lengths and also angles) or irregular(with 6 unequal side lengths and angles).

Hexagons deserve to be classified based on their side lengths and internal angles. Considering the sides and also angles that a hexagon, the types of the hexagon are,

Regular Hexagon: A continuous hexagon is one that has equal sides and also angles. All the internal angles of a regular hexagon are 120°. The exterior angles measure 60°. The amount of the internal angles of a consistent hexagon is 6 time 120°, i m sorry is equal to 720°. The sum of the exterior angle is same to 6 time 60°, which is same to 360°.Irregular Hexagon: An irregular hexagon has sides and also angles of various measurements. All the internal angles are not same to 120°. But, the amount of all internal angles is the same, i.e 720 degrees.Convex Hexagon: A convex hexagon is one in which all the internal angles measure much less than 180°. Convex hexagons deserve to be regular or irregular, which method they deserve to have equal or unequal side lengths and also angles. All the vertices that the convex hexagon are pointed outwards.Concave Hexagon: A concave hexagon is one in which at least one the the internal angles is greater than 180°. There is at least one vertex the points inwards.

A hexagon is a flat two-dimensional form with six sides. It might or may not have equal sides and also angles. Based on these facts, the important properties that a hexagon space as follows.

It has actually six sides, six edges, and six verticesAll the next lengths space equal or unequal in measurementAll the internal angles are equal come 120° in a consistent hexagonThe sum of the internal angles is always equal come 720°All the external angles are equal come 60° in a continual hexagonSum that the exterior angles is equal to 360° in a hexagonA continuous hexagon is likewise a convex hexagon due to the fact that all its interior angles are less than 180°A consistent hexagon have the right to be separation into six equilateral trianglesA continual hexagon is symmetrical together each the its next lengths is equalThe opposite sides of a consistent hexagon are constantly parallel to every other.

As with any polygon, a continual hexagon also has a different formula to calculation the area, perimeter, and a variety of diagonals. Let united state look into each among them.

### Diagonals that a Hexagon

A diagonal is a segment that a line, the connects any two non-adjacent vertices the a polygon. The number of diagonals the a polygon is offered by n(n-3)/2, where 'n' is the number of sides the a polygon. The variety of diagonals in a hexagon is given by, 6 (6 - 3) / 2 = 6(3)/2, which is 9. The end of the 9 diagonals, 6 of them pass through the facility of the hexagon.

### Sum of internal Angles the Hexagon

The amount of internal angles formed by a continuous hexagon is 720˚ (because each angle is 120˚ and there room 6 together angles adding up come 720˚). The is provided by the formula for continual polygon, wherein n is a number of sides, which has a worth of 6 because that hexagonal shape. The formula is (n-2) × 180°. Therefore, (6-2) ×180° which provides us 720°.

The area of a consistent hexagon is the an are or the an ar occupied by the shape. It is measure up in square units. Let united state divide the hexagon right into 6 equilateral triangles as presented below. Let united state calculate the area of one triangle and multiply that by 6 to gain the entire area that the hexagon.

Area the one it is intended triangle is √3a2/4 square units. Hence, the area of a regular hexagon developed by combine 6 together triangles is,

6 × √3a2/4= 3√3a2/2 square units

Therefore, the formula because that the constant hexagon area is 3√3a2/2 square units.

### Perimeter that a Hexagon

Perimeter is the full length of the border or the outline of a shape. Considering the side of a regular hexagon as 'a' units, the consistent hexagon perimeter is given by summing up the size of every the political parties which is equal to 6a units. Therefore, the perimeter the a regular hexagon = 6a units, and also the perimeter the an rarely often, rarely hexagon = (a + b + c + d + e + f) units, where, a, b, c, d, e, and f are the side-lengths the the hexagon.

☛ Topics related to Hexagon

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Example 1: What is the area the a constant hexagon with sides equal to 3 units?

Solution:

Area of a constant hexagon = 3√3a2/2 square units.Given side 'a' = 3 unitsTherefore, area = 3(√3)32/2= (3 × √3 × 9) /2= (27× √3) / 2= 23.382 square units,

Example 2: uncover the size of each side the a continuous hexagon, if the hexagon's area is 1503 square units. Usage the length of the political parties to find the perimeter the the hexagon.

Solution:

Applying the formula that area the a continual hexagon,

Area that a consistent hexagon = 3√3a2/2 square units.Therefore, 150√3 = 3√3a2/2300√3 = 3√3a2Canceling √3 on both sides,300/3 = a2100 = a2a = √100Therefore, the size of every side, a = 10 units.

Therefore, the length of the political parties of the hexagon = 10 units.Perimeter the a consistent hexagon = 6a units.a = 10 units. Therefore,Perimeter = 6 × 10Therefore, the given consistent hexagon perimeter = 60 units.

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