You will need

- - the range;
- a pair of compasses.

Instruction

1

To find the perimeter

**of the hexagon**, measure and add the lengths of all six sides. P = A1+A2+A3+A4+A5+A6,where P is the perimeter**of the hexagon**, and A1, A2 ... A6 – the length of its sides.The units of each of the parties reduced to a single species, in this case, it is sufficient to store only the numerical values of the lengths of the sides. The unit of measure of the perimeter**of the hexagon**will coincide with the unit of measure of the parties.2

Example.A hexagon with side lengths 1 cm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm. is Required to find its perimeter.Solution.1. The unit of measurement of the first side (cm) differs from the units of measurement of the lengths of the other sides (mm). Therefore, move: 1 cm = 10 mm. 2. 10+2+3+4+5+6=30 (mm).

3

If the hexagon is correct, then to find its perimeter, multiply the length of its side six:R = a * 6,where a is the length of sides of a regular

**hexagon**.Example.To find the perimeter of a correct**hexagon**with side length equal to 10 cm Solution: 10 * 6 = 60 (cm).4

A regular hexagon has a unique feature: the radius of the circumscribed around this

**hexagon**of a circle is equal to the length of its side. So, if you know the radius of the circumscribed circle, to use the formula:P = R * 6,where R is the radius of the circumscribed circle.5

Example.To calculate the perimeter of a right

**hexagon**, wrote in a circle of diameter 20 cm Solution. The radius of the circumscribed circle will be equal to: 20/2=10 (cm).Therefore, the perimeter**of the hexagon**: 10 * 6 = 60 (cm).6

If a task is set to the radius of the inscribed circle, apply the formula:P = 4 * √3 * r,where r is the radius inscribed in a regular hexagon circle.

7

If you know the area of the right

**hexagon**, then to calculate the perimeter use the following ratio:S = 3/2 * √3 * A2,where S – area of a regular**hexagon**. Here you can find a = √(2/3 * S / √3), hence:P = 6 * a = 6 * √(2/3 * S / √3) = √(24 * S / √3) = √(8 * √3 * S) = 2√(2√3).# 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

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

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

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

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

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