Instruction

1

*diagonal/em/b" class="colorbox imagefield imagefield-imagelink" rel="gallery-step-images">*Rectangular quadrilaterals (rectangle, square) the diagonal divides into two right-angled triangles, in each of which she will be the hypotenuse. Therefore, for calculating it is possible to use the Pythagorean theorem. a2=b2+c2, where a is the hypotenuse, b and C are the legs. Example 1: find the diagonal AC , if you know that length BC=3 cm, AB=5 cm Solution: calculate the hypotenuse AC in right triangle ABC. AC2=AB2+BC2; AC2=52+32=34; from this value, extract the square root of a: AC=√34=5.8 to see the Answer: the diagonal of the rectangle is equal to 5.8 cm

2

*If you see a square, then calculate the diagonal is possible, knowing one of its sides or the square. Since all the sides of the square are equal, the Pythagorean theorem is: a2=b2+b2, a2=2b2. Square - the product of two sides (S=b2). Hence, the square of the hypotenuse (in the figure the square) equal to twice the area (a2=2S).Example 2: the area of a square is 16 cm2. Find*

**the length**

**. Solution: calculate**

*of the diagonal***the length**

**and through the area. a2=2S, a2=2*16 cm2=32; extract the square root a=√32≈5.7 cm answer: the length of**

*of the diagonal***of the square – 5.7 cm**

*the diagonal*3

*In some cases, to compute*

**necessary to make additional construction.Example 3: an equilateral polygon with sides equal to 6 cm, angle BCD straight. Find**

*the diagonals***the length**

**AB.Solution: connect points B and D. it Turned out a right triangle BCD in which side BD is the hypotenuse. Calculate the hypotenuse BD: BD2=BC+CD2; BD2=62+62=72; the Hypotenuse BD of the triangle BCD is the leg of the triangle ABD. And the diagonal AB is the hypotenuse in it. Calculate diagonal AB: AB2=BD2+AD2=72+36=108; AB=√108=10,4 cm a: length**

*of diagonal***AB=10,4 cm**

*of diagonal*4

*The diagonal of a cube can be found using the diagonal of one of its faces.Example 4: a cube with side 5 cm Find the diagonal of the cube.Solution: extend and calculate the diagonal of the cube face. AC2=52+52=50. The diagonal AC is perpendicular to the edge of the CB, therefore the angle ACB is a straight line. Diagonal cube AB is the hypotenuse of the triangle ACB. Find*

**the length**

**of cube: AB2=AC2+CB2=50+25=75; extract the square root. AB=√75=8,7 cm answer: the length of**

*of diagonal***of a cube is 8.7 cm**

*the diagonal*5

*To calculate the diagonals of a parallelogram using the theorem of cosines: c2=a2+b2-2ab*cosy.Example 5: a = 2 cm b = 3 cm, γ = 120°. Find the diagonal of s. Solution: substitute the values into the formula. c2= 22+32-2*2*3*cos120°; cos120° look at the table of cosines at (-0.5). S2 = 4+9-12*(-0,5)=13-(-6)=19. From this value, extract the root: C = √19 = 4,35 see Answer: length*

**= 4,35 cm**

*of diagonal*# Advice 2: How to calculate the area of a cube

The cube is a special case of a parallelepiped, in which each of the faces formed by the right polygon is a square. Only the cube has six faces. To calculate the area is not difficult.

Instruction

1

Initially, you need to calculate the area of any squares, which is a face of this cube. The area of a square can be calculated by multiplying at each other a couple of its sides. The formula can be expressed as:

S = a*a = a2

S = a*a = a2

2

Now that we know the area of one of the edges of the square, you can see the area of the whole surface of the cube. This can be done by modifying the formula listed above:

S = 6*a2

In other words, knowing that such squares (faces) of the cube have as many as six pieces, the surface area of the cube is one of the areas of the faces of the cube.

S = 6*a2

In other words, knowing that such squares (faces) of the cube have as many as six pieces, the surface area of the cube is one of the areas of the faces of the cube.

3

For clarity and convenience, you can give an example:

For example, given a cube whose edge length is 6 cm, it is required to find the surface area of this cube. Initially you will need to find the area of the face:

S = 6*6 = 36 cm2

Thus, knowing the area of the face, you can find the entire surface area of a cube:

S = 36*6 = 216 cm2

Answer: the surface area of a cube with an edge equal to 6 cm is 216 cm2

For example, given a cube whose edge length is 6 cm, it is required to find the surface area of this cube. Initially you will need to find the area of the face:

S = 6*6 = 36 cm2

Thus, knowing the area of the face, you can find the entire surface area of a cube:

S = 36*6 = 216 cm2

Answer: the surface area of a cube with an edge equal to 6 cm is 216 cm2

Note

The cube is a special case not only of a parallelepiped, and prisms.

A parallelepiped is the prism whose base is a parallelogram. Feature of box is that 4 of its 6 sides - rectangles.

Prism is the polyhedron whose base are equal polygons. One of the main features of the prism can be called that the side faces is a parallelogram.

In addition to Cuba, there are other types of polyhedra: pyramids, prisms, parallelepipeds, etc., each of which correspond to different ways of finding the areas of their surfaces.

A parallelepiped is the prism whose base is a parallelogram. Feature of box is that 4 of its 6 sides - rectangles.

Prism is the polyhedron whose base are equal polygons. One of the main features of the prism can be called that the side faces is a parallelogram.

In addition to Cuba, there are other types of polyhedra: pyramids, prisms, parallelepipeds, etc., each of which correspond to different ways of finding the areas of their surfaces.

Useful advice

If not given cube, and another is a right polyhedron, in any case, the surface area will be similar. This means that the surface area of regular polyhedron is found by adding together all the areas of its faces regular polygons.

# Advice 3: How to calculate the diagonal of the rectangle

Rectangle is one of the simplest of geometric shapes, which, having all the angles equal to 90°, is a special case of a parallelogram. The segment connecting two vertices of a rectangle having a common side is called a diagonal of this polygon. To calculate the length of the diagonal in several ways depending on the known source data.

Instruction

1

If you know the lengths of both sides (A and B) of the rectangle, then the length of the diagonal (C) can be defined as the square root of the sum of the squares of the lengths of the sides. This follows from the Pythagorean theorem, since the diagonal in this geometric figure forms a right triangle the other two sides of which are sides of the rectangle. The diagonal of this triangle is the hypotenuse, and the sides of the rectangle are the legs. That is: C=√(A2+B2).

2

If the length of one side is unknown, but the known length of the other (A) and area (S) of the rectangle, the diagonal length can also be calculated. Since the area of a rectangle is found by multiplying the lengths of its sides, the unknown side can be expressed as the quotient of the square of the length of the other side. Substitute the expression obtained in the first step the formula: C=√(A2+S2/A2)=√(A⁴+S2)/A.

3

If you know the length of one side of the rectangle (A) and the length of its perimeter (P), the length of the second side can also be determined. Since the perimeter of a rectangle is twice the sum of the two sides, then each side can be defined as the difference between pauperisation and a length of the other side. Substitute this expression in the same formula from the first step: C=√(A2+(P/2-A)2=√(A2+P2/4-P×A+A2)=√(2×A2+P2/4-P×A).

4

If you know the radius of the circle (R) containing the rectangle, its diagonal will be equal to twice the radius, as the center of the rectangle and the circle in this case are the same. The line connecting the two points of the circle and passing through its centre is equal to its diameter, i.e. the two radii. And since the vertices of this rectangle lie on the circle, and the connecting diagonal passes through the centre, it is also consistent with the definition of the diameter of a circle: C=2×R.

5

If you know the radius of the inscribed rectangle of the circle (r), then the lengths of its sides are the same. This is a special case of rectangle called a square. To determine the length of the parties in this case as twice the length of the radius of the circle, and substituting this expression into the formula from the first step, you will get: C=√(4×r2+4×r2)=r×√8.

# Advice 4: How to calculate the thief in the team

Unfortunately, sometimes even in the most cohesive and close-knit groups appear thieves. Colleagues are beginning to carefully look at each other, trying to figure out who is stealing things and money. And often it turns out that and think no one, but the loss continues.

You will need

- a small video camera (e.g., mobile phone).

Instruction

1

Contact security service. The employees of this Department can help in the calculation

**of the thief**. They'll conduct an internal investigation and after a certain time can give you the name of the offender. However, the security may not always help you in this matter.2

Attentively get accustomed to colleagues. Look at the behavior of each employee. Eyes

**of a thief**often "run" in search of profit, and if he will lock eyes with you, he will immediately take the eye.3

Talk with each employee. Alone tell your colleague that you know exactly what a thief is he, and his reaction and behavior. Evidence and proof you are unlikely to find, but these conversations will help you to figure out who is stealing valuable things.

4

Get a special powder and a flashlight. This powder is treated money. And when a man touches them, his hands would leave marks that can be seen using ultraviolet light. To calculate

**the thief**must leave the marked bills in a prominent place, and when they lost, Shine on the hands of the employees.5

Install a hidden camera. The intended action is important to tell your colleagues - it should be done in secret, otherwise the thief finds out about the impending trap. Set the camera to the place from which a clear view of the entire room. So you will be able to obtain irrefutable proof of guilt of a specific employee.

6

Go to the police. When theft occur regularly and calculate

**the thief**alone does not work, you can contact the police. However, even the police are not always able to help you. Of course, they will hold a conversation with each employee, but is unlikely to be able to find**the thief**immediately. They can give special wallets filled with paint. When the wallet is opened, the package contained inside is broken and indelible ink splashed in the face**of the thief**.# Advice 5: How to find the diagonal of the TV

**Diagonal**

**of the TV**is useful to know. About it will ask the repair centre if the unit will need resuscitation. Given diagonal it is necessary to choose the distance at which you can sit in front of the screen.

You will need

- TV
- centimeter/roulette
- calculator
- - manual
- - Notepad and pen

Instruction

1

To know the diagonal of your TV, you can use several ways. The first and most basic is to look in the instructions to the apparatus or even on the box. Right on the cover of the user's guide specified the brand of TV, model and its diagonal.

2

It happens that neither the box nor the instructions can not be found. In this case, accurately determine what TV presented to measure: CRT (TV CRT), LCD (LCD) or plasma.

3

If you have a CRT TV, then measure the diagonal it is necessary for the glass of the bulb. Just pull the cm from one corner diagonally to another. Record the result in centimeters.

4

LCD/plasma TV before measurement it is necessary to include. Get away from him a meter and a half, look fix extreme luminous pixels in the corners. The fact that LCD and plasma TVs, the image is enclosed in a small black frame around the perimeter of the TV. So the measurements should be carried out at the most distant from each other pixels.

5

Turning off the TV, walk up to him. Apply cm from one extreme of a luminous pixel diagonally through the screen to the other. Write down the result.

6

Produce the calculations. Diagonal TV or monitor is always stated in inches. To know the right size, divide the centimeters by 2.54 see the data the result will be the diagonal of your TV.

Note

If you measure the diagonal of the TV with a tape, don't put it close to the screen. The metal can scratch the coating.

Useful advice

To accurately measure the diagonal of the TV difficult enough, so don't be surprised if you get strange number. For the reliability of the result, round it up or down.

# Advice 6: How to calculate the length of triangle side

To calculate lengths of sides in an arbitrary triangle most often has to apply the theorem of sines and cosines. But among the whole set of arbitrary polygons of this kind there are of them "more correct" variations - equilateral, isosceles, rectangular. If the triangle is known that it belongs to one of these species, methods of calculation of its parameters is much easier. When calculating the lengths of their sides is often possible to do without trigonometric functions.

Instruction

1

**The length of the**

**side**(A) of an equilateral

*triangle*to find the radius of the inscribed circle (r). To do so, increase it to six times and divide by the square root of triples: A = r*6/√3.

2

Knowing the radius of the circumscribed circle (R), too it is possible to calculate the length of

**side**(A) right*triangle*. This radius is twice that used in the previous formula, so triple it and also divide by the square root of triples: A = R*3/√3.3

The perimeter (P) of an equilateral

*triangle*to calculate the length of its**side**(A) is even simpler, because the lengths of the sides in this figure are the same. Just divide the perimeter into three pieces: A = R/3.4

In an isosceles triangle the calculation of the length

**of the sides**of known perimeter is a bit more complicated - you need to know more and a length of at least one of the parties. If you know the length**of side**A lying in the base of the figure, the length of any side (In) find halving the difference between the perimeter (P) and the size of the base: B = (R-A)/2. And if you know the side, the length of the base define by subtracting from the perimeter to twice the length of the side: A = R-2*V.5

Knowledge area (S) occupied on the plane right triangle, is also sufficient for finding the lengths of its

**sides**(A). Extract the square root of the area ratio and the square root of three, and the result double A = 2*√(S/√3).6

In a right triangle, unlike any other, to calculate the length of one of the parties is sufficient to know the lengths of the other two. If the target side is the hypotenuse (C), to do this, find the square root of the sum of the lengths of the known sides (A and b) squared: C = √(A2+B2). But if you want to calculate the length of one of the other two sides, then the square root must be obtained from the difference of the squares of the lengths of the hypotenuse and another side: A = √(C2-B2).