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

Hexagonal - the "hexagonal" form, for example, have a section of nuts and pencils, honeycomb and snowflakes. A regular geometric shape, such shapes have certain features that distinguish them from other flat polygons. It consists in the fact that the radius of the hexagon described about a circle equal to the length of its sides, in many cases, this greatly simplifies the calculation of the parameters of the polygon.
How to find the side of a regular hexagon
Instruction
1
If the conditions of the problem given the radius (R) described about the right of the hexagon of a circle, calculate do not have - this value is identical with the length of the side (t) of the hexagon: t = R. in the case of known diameter (D) simply divide it in half: t = D/2.
2
The perimeter (P) the right of the hexagon allows us to calculate the length of a side (t) by a simple operation of division. As divider use the number of parties, i.e. six: t = P/6.
3
The radius (r) inscribed in a polygon circle is associated with the length of its side (t) is slightly more complex ratio - double the radius, and the result divide by the square root of triples: t = 2*r/√3. The same formula using the diameter (d) of the inscribed circle will be one mathematical operation in short: t = d/√3. For example, if the radius of 50 cm side length of the hexagon should be approximately equal to 2*50/√3 ≈ 57,735 see
4
Known area (S) of a polygon with six vertices also allows us to calculate the length of its side (t), but the numerical factor linking them, just expressed through the fraction of three natural numbers. Two thirds of the area divide by the square root of three, and the obtained values remove the square root: t = √(2*S/(3*√3)). For example, if the area of the figure is 400 cm2, the length of her hand should be about √(2*400/(3*√3)) ≈ √(800/5,196) ≈ √153,965 ≈ 12,408 see
5
The circumference (L) described around the right hexagon, connected with the radius and, therefore, with side length (t) through the number PI. If it is given in terms of the problem, divide its value by two PI is: t = L/(2*π). For example, if this value is equal to 400 cm, side length should be approximately 400/(2*3,142) = 400/6,284 ≈ 63,654 see
6
This is the same parameter (l) for the inscribed circle allows you to calculate the length of a side of the hexagon (t) by calculating the ratio between it and the product of the number PI by the square root of triples: t = l/(π*√3). For example, if the length of the inscribed circle is 300 cm, the side of the hexagon needs to have a value approximately equal to 300/(3,142*√3) ≈ 300/(3,142*1,732) ≈ 300/5,442 ≈ 55,127 see

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.
How to find the area of the hexagon
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

Advice 3: How to find a life-size section

Properties of figures in space involved in this section of geometry, as geometry of space. The basic method for solving problems in solid geometry is a method of cross-section polyhedra. It allows you to correctly build the cross-section of the polyhedra and to determine the species of these sections.
How to find a life-size section
Instruction
1
The definition of the cross-section of any shape, that is, the actual size of this cross-section, often assumed in formulating the tasks of building a sloping section. The oblique section should be called front-secant projective plane. And build it life-size enough to perform several actions.
2
With a ruler and pencil, draw in figure 3 the projections – front view, top view and side view. The main projection in the front view show the path that is front-projecting section plane, draw a sloping line.
3
On an incline direct select main points: points of entry section and exit section. If a figure is a rectangle, the points of entry and exit will be one. If a figure is a prism, then the number of points is doubled. Two points define the entry into and figure out. The other two identify points on the sides of the prism.
4
At an arbitrary distance guide line parallel to the front projecting section plane. Then, from the points located on the axis of the main view, swipe to the auxiliary line perpendicular to the inclined straight line until they intersect with the parallel axis. Thus you will get the projection of the points of the shape in the new coordinate system.
5
To determine the width of the figure, lower straight from the main point of view the figure of top view. Indicate the appropriate indices of the projection points at each intersection of a line and a shape. For example, if point a belongs to the mind of the figure the points A’ and A” belong to projective planes.
6
Put in the new coordinate system the distance that is formed between the vertical projections of the main points. The figure, which is obtained as the result of development, and is a natural value of the inclined section.
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