How to calculate the area of ​​a room

Someone probably seem ridiculous as "childish" question - "how to calculate the area of ​​a room."But let's accept the fact that, firstly, many of us were finishing school for a long time.Secondly, not everyone in everyday life are constantly faced with the need for geometric calculations , and something that might have forgotten.And, thirdly, the room and the walls are not always and not everywhere have a rectangular shape with an area to calculate quickly and easily.So sometimes have to show ingenuity and apply more sophisticated calculation methods.

And what do need to be able to determine floor space, walls and ceiling of the room?

• These data are necessary for the planning of repairs in the apartment - it is possible to calculate the number of required construction materials.
• If the work is done by hired masters, they often require payment per square meter.To avoid becoming a victim of fraud, be able to monitor the integrity of employees and not to pay too much, you must be able to correctly identify
  volume of work performed.
• Numeracy construction schemes and to define the area may be necessary when viewing premises options presented for sale or lease.By the way, and the amount of the payment of some public services also depends on the size of it is useful and common area.
• correct selection of lighting depends on the area of ​​the room - this account, there are special regulations illumination.
• Knowing the area, it is easy to calculate the volume and premises.A it - the main parame tr etc. and selection of heating appliances, HVAC equipment, ventilation systems.

In short, this skill never hurts.And if the reader went on this page, means it took him to learn or brush up on calculation algorithms area.Therefore , begin to consider, according to the principle "from simple - to difficult".

Preparing for calculations

This stage, in fact, includestwo main points.Needed to prepare the area where the measurement of work required for this tools and accessories, and in fact, to conduct measurements, transferring the results to a scheme or drawing .

• Ideally, it is best to carry out all the measurements in a fully liberated from furniture and other room items.When the repair is usually so happens.But if the measurement is carried out for purposes other then to make all of the room, of course, no one will undertake.

measurements lengths of the sides of the room is usually carried out along the walls.Therefore , you must try to free these areas, so that you can fully, from wall-to-wall , stretch the tape measure tape.

• Check squareness of the room to perform the easiest sounding diagonal.Therefore , you may need the space in the center of the room.Or it should be possible to move objects that could be a hindrance for the measurements.

follow certain ironic remarks - really the author by giving such advice, never heard of the modern electronic laser roulette?Of course, these modern devices not only help to quickly and accurately measurement of linear and angular values ​​- many of them have built-in features make the necessary calculations .

But let's "Down to earth» - such instrument has so far not many.Professionals, yes, without it is currently difficult.However, in a domestic environment, while the majority of people rely on the traditional measurement methods.Incidentally, for measuring laser tape measure space anyway all still create have - for the smooth passage of the beam.

• So assume that measurements are usually carried out with a tape measure.In addition to notepads can need :

- long line spacing for straight lines (for example, a rule can go long or building level);

- maximum large (greater than - the better) building square;

- improvised compasses - it can be a lasting piece of string tied to any sharp pin, which will play the role of the center;

- to measure the angle - or need a special tool, or hold calculations using trigonometric functions.However, in those methods to be offered, the measurement of the angle does not become a mandatory procedure - dispense linear values.

- may be needed on the ground to carry out some supporting markup.To not dirty the floor with chalk or marker, you can use a thin masking tape.

• All measurements are best done twice - so it will be less likely to prevent any annoying error inadvertently.
• roulette tape during the measurements should not sag, on the measurement site must be a straight line, to stretch .

• Focus on the scale!Do not confuse the metric system and "inch - foot", as many measuring tools applied both scales.
• work will be much easier if pre-sketch a rough plan of the premises on paper. Not necessarily his plot in this case super-neat , on a scale to meet the requirements of the drawing standards.

just become much easier to transfer measurement results directly to the paper, for further calculations .

When measuring distances will need to record them in meters, rounded to the nearest centimeter, for example, 0, 82 m or 5, 38 m .Then all at once the results are obtained in the desired square meters.

• Some formulas for calculating - rather cumbersome, containing reflux rigonometricheskie function or calculate square roots, that is, "in a column" does not get counted.Well, if you have the ability to carry out calculations to Excel - all clearly, plus the entire process can be saved in a file.If not - means set in motion calculator.It is convenient to use that is built into Windows - just be sure to translate it from "normal" to "engineering" through the "View" menu, or by simultaneously pressing the buttons «Alt + 2."

mode now proceed to consider possible options for the configuration of the room.

Determine room floor area

Rectangle

1. Probably the most common configuration of the room, especially in urban high-rise buildings.And, accordingly, the most simple way to calculate area.

side of the rectangle can be described as A and B. Thus, the area will be equal to:

S = A × In

Opposingsides of the rectangle are equal in pairs, that is, in fact, can only measure the two values.

But we must not forget about checking - and whether it is a rectangle?You can attach to each corner of the square building, but this is not always gives clear picture.Simply will make diagonal measurements and compare the results.If they are the same or the difference is quite small, it can be assumed that this is really a rectangle.

In the present example, the room area is:

S = A × In = 5,82 × 3,77 = 21,94 m²

2. room can have projections, niches and passageways etc . rectangular shape.Do not worry - it is possible to break the scheme a total area of ​​several rectangles.It is understood that after the area calculation on sites all the values ​​are summed.

The diagram shows an example of the vast space with a protruding portion.The diagram in red dotted line shows the division of the room into two rectangular plot.It remains only to find the area of ​​each and summarize its :

Σ s = S 1 + S 2 = 8.26 × 3.73 + 2.63 × 1.50 = 30.81 + 3.95= 34.75 m²

3. Sometimes it happens that the protrusion on the contrary , to the room side and therefore "eats" part of the area.

Then when calculations can go through other - to find the area of ​​the "stolen" space and subtract it from square large rectangle.

Trapeze

This situation often happens in the corner areas.

characteristic feature quadrangle , called trapezoid - the two sides of it are parallel to each other, and the other two can be arranged at an arbitrary angle.

In this case to determine the area you need to know three parameters - the length of two parallel sides of the trapezoid, and the height, ie the perpendicular distance between them.

S = ½ ( A + B ) × h

This formula is universal - from the sides of the angle, nothing changes, and their importance to us to knownot necessary.But the height h better fathom in several places - will have confidence that the two sides really are parallel to each other.

Consider this example:

typical trapezoidal room.Making measurements and apply the formula:

S = ½ ( A + B ) × h = 0,5 × (6,27 + 7,00) × 2,73 = 15,83 m²

Sometimes knowledge of the formula area of ​​a trapezoid and is useful for complex, polygonal shape of the room.For example, below is shown in the drawing pentagonal room.Her most conveniently divided into two sections - a rectangle and a trapezoid (notional divided by the red line).

area rectangle:

S 1 = 6.33 × 3.95 = 25 m²

One of the sides of the rectangle and a trapezoid base.A trapezoid height - the difference of the lengths of the opposite sides of the room:

h = 7.71 - 6.33 = 1. 38 m

find the area of ​​the trapezoid:

S 2 = 0.5 × (3.95+ 2.55) × 1.38 = 5. 71

total area of ​​the whole premises is:

Σs = S 1 + S 2 = 25.0 + 5.71 =30. 71

calculator to calculate the area of ​​a rectangular or trapezoidal space

The following calculator allows you to calculate the area of ​​a rectangular and trapezoidal rooms - the only difference that the value of the lengths of the rectangular A1 and A2 will same.

calculator, if necessary, immediately possible to make amendments to the existing niches or projections.

Triangles

Until now, in all the examples observed some "correct» - premises or rectangular, or, at least, have parallel walls.And what if the complex shape of the room does not allow it divided into such "correct" figure?

Do nothing, have broken into triangles completely form the derivative, and then turn calculate their area and to summarize.

triangle area actually calculate simple - it is necessary to multiply the length of the base perpendicular to the base height, carried out from the opposite angle, and divide by two.

S = ½ × and × h

difficulty is that just beat off the perpendicular height under measurements on the floor, large distances, but still and without special tools - not so simple.You can easily make a purely geometrical error, which drags a wrong result calculated area.

In this case it is better to use Heron's formula for triangles.It is, however, somewhat cumbersome, but it allows you to pinpoint the area solely on the basis of the lengths of sides of a triangle.It looks so:

S = √ p × (p - a) × ( p - b) × ( p - c )

where:

- and , b and with - the length of the sides of the triangle;