Advice 1: How to find the area of a regular hexagon

A regular hexagon is a geometric figure in the plane, with six equal sides. All the corners of this shape is 120 degrees. The area of a regular hexagon is very easy.
Instruction
1
Finding the area of a regular hexagon is directly related to one of its properties, which says that around this figure can describe a circle and fit it inside this hexagon. If the inside of a regular hexagon inscribed circle, the radius can be found by the formula: r = ((√3)*t)/2, where t is the side of the hexagon. It should be noted that the radius of the circle circumscribed around the regular hexagon, is equal to its side (R = t).
2
Once is the radius of inscribed/circumscribed circle, you can begin finding the area of the desired shape. To do this, use the following formulas:
S = (3*√3*R2)/2;
S = 2*√3*r2.
3
To find the area of this shape have not caused trouble, consider a few examples.
Example 1: Given a regular hexagon whose side is equal to 6 cm, it is required to find its area. For the solution you can use in several ways:
S = (3*√3*62)/2 = 93.53 cm2
The second method is more long. First, find the radius of the inscribed circle:
r = ((√3)*6)/2 = 5.19 cm
Then use the second formula to find the area of a regular hexagon:
S = 2*√3*5.192 = 93.53 cm2
As you can see, both ways are valid and do not require to check their solutions.

Advice 2: How to find the area of the hexagon

By definition of the right of plane geometry a polygon is a convex polygon whose sides are equal and angles are also equal. A regular hexagon is the right polygon with number of sides equal to six. There are several formulas for calculating the area of a regular polygon.
Instruction
1
If you know the radius of the circle circumscribed about a polygon, then its area can be calculated by the formula:

S = (n/2)•R2•sin(2π/n), where n is the number of sides of the polygon, R is the radius of the circumscribed circle, π = 180º.

In a regular hexagon all the angles equal to 120°, so the formula would be:

S = √3 * 3/2 * R2
How to find the area of the hexagon
2
In the case where a circle with radius r is inscribed in a polygon, its area is calculated by the formula:

S = n * r2 * tg(π/n), where n is the number of sides of the polygon, r is the radius of the inscribed circle, π = 180º.

For hexagon, this formula takes the form:

S = 2 * √3 * r2
How to find the area of the hexagon
3
Area of a regular polygon can also be calculated knowing only the length of its sides using the formula:

S = n/4 * a2 * ctg(π/n), n is the number of sides of the polygon, a is the length of sides of the polygon, π = 180º.

Accordingly, the area of the hexagon is equal to:

S = √3 * 3/2 * a2
How to find the area of the hexagon
Note
It is impossible not to notice the prevalence of the form of a regular hexagon in nature. Just think of honeycomb. Almost all the complex carbon molecules have a regular hexagonal shape. Even in chemistry when portraying a molecule of benzene, used the same form.

One of the properties of a regular hexagon says: it is possible to tile any plane. This property is widely used tile pavers all countries that can pave any sidewalk tile that is hexagonal shape.
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