How to calculate the area of a room and roof of different configurations
When repairing, arranging an apartment or house, you should know exactly how much building materials should be purchased. Let's consider how to calculate the area of a room that has a classic rectangular shape and non-standard geometry, including protrusions and niches. We will also deal with roofs of popular forms: single-slope, double-slope, hip or four-slope and their varieties. For measurements, you will need a tape measure, for calculations - any calculator, a piece of paper with a pen or pencil and mathematical formulas for grade 6.
How to calculate the area of a room
Rectangular rooms
The calculation algorithm is the simplest. For the floor and ceiling (they usually have the same dimensions):
- measure the width and length of the room in an accessible place (where furniture will not interfere);
- multiply the width by the length, and you get the coveted value.
For walls, measure their height and length. To calculate the area of all walls, measure the dimensions of one, then the second, located next to each other, calculate the area of each of them, sum and multiply by 2.
For example, the dimensions of the room are as follows: 3 × 4 and 4 × 5 meters. The square of the smaller wall is 3 * 4 = 12 m2, larger - 4 * 5 = 20 m2... Total wall area - 2 * (12 + 20) = 64 m2.
To exclude overspending of material (paint, wallpaper), subtract the area of window and door openings from the obtained value.
It is also important that the units are the same. If the width was measured in meters, for example, it turned out to be 4.35 m, then the length should be taken in meters.
A square meter is equal to 10,000 square centimeters, not 100 cm, as you might expect. 1 m = 100 cm, and 100 cm × 100 cm = 10,000 cm2... When translating values from cm2 in m2 and vice versa, remember this and shift the comma in the appropriate direction.
Depending on the required accuracy, one or two digits are left after the decimal point, rounding the value up.
In old wooden houses often, the main beams adjacent to the walls are masked with a large amount of putty or decorated with wood, plasterboard and other materials. For such cases, the height measurement becomes more difficult. The way out of the situation is to use a plumb line or make approximate measurements, if high accuracy is not needed.
Rooms with a niche or ledge
Knowing how to calculate the area of a rectangle, you can calculate any surface in a house or apartment. Floor to ceiling and opposite walls are usually equal in size. If there are non-standard openings, for example, an arch, to simplify calculations, its shape can be neglected: calculate a rectangular opening. If this is unacceptable, look for recommendations on arches in a couple of sections below.
Protrusions and niches are usually rectangular in shape and are easy to calculate. It is important not to forget about the side surfaces, because many take into account only the main one (in the figure it is colored in orange).
Non-standard solutions
Not everyone lives in properly shaped houses and rooms. In such situations, the surface is divided into the minimum possible number of geometric shapes (usually rectangles, less often triangles), the area of each of them is calculated, and the obtained values are summed up.
Circle, oval
To calculate a round surface, find its center and measure the radius (or diameter and divide it in half).
The area of a circle is calculated by the formula: S = πR2, where π ~ 3.1415.
There are a little more operations with an oval. Measure the distance from its center to the major and minor semiaxes - the nearest and farthest edges. Multiply the measured values among themselves, and then by the number π. The formula looks like this: S = a × b × π.
Triangle
In the case of a right-angled triangle, the area is calculated using a simple formula: S = (a * b) / 2, where a and b are the lengths of the sides forming an angle of 900 - half the area of the rectangle.
When there is no such angle, use Heron's formula: S = √p (pa) x (pb) x (pc), where a, b, c are the lengths of the sides of the figure, and p is its half-perimeter - half the sum of the sides: (a + b + c) / 2.
Arch and segment
Arches usually look like a semicircle with a rectangle as a continuation. The size of such a structure is subtracted from the surface area of the wall. First, break it down into the simplest geometric shapes, calculate and sum the areas of their surfaces. The semicircle is calculated by the formula: πR2, rectangle: S = a × b or a × d, where d is the diameter of the circle - it is the length of one side of the rectangle.
Sometimes arches are made in the form of a segment of a circle, not a sector.
And its dimensions are easily determined without complicated calculations using the formula:
S = R² × arcsin (C / 2R) - 0.25 × C × √ (4R² - C²), where C is the chord length.
Based on the height of the segment H, you must first calculate the distance L: L = R - H. Substitute the known values into the formula: S = R² × arccos (L / R) - L × √ (R² - + L²).
We use smart devices to calculate the area - video
How to calculate the roof area
It is more difficult with the roof: measurements cannot always be performed, usually there are more calculations than with the walls and floor, the ceiling of the room.
Shed
The simplest and most economical roof option, houses with this shape are rarely built, more often outbuildings and sheds. Find out the area shed roof can be done in two ways. The first involves measuring and multiplying its width by length, to which overhangs are added.
If the length of the building is unknown, it is easily determined thanks to the Pythagorean theorem: C =√A2+B2.
Gable
If the slopes of the building are the same, you need to calculate the area of one and multiply it by two. When they differ, calculate the sizes of each one as described above and add the resulting values.
Four-slope
Hip and hip roofs are common types of hipped roofs. The hip roof is used for houses that have a rectangular shape, and the hipped roof is used for square ones (in fact, it is a kind of hip roof). The latter has a pair of triangular slopes and a pair of trapezoidal ones.
To calculate the area of a trapezoid, measure the lengths of the parallel sides and the distance between them - the segment that lies between them at right angles:
Triangles are calculated using Heron's formula or an isosceles triangle. The total roof surface area consists of the sum of the areas of a pair of triangles and two trapezoids with equal sides (not bases).
When calculating the roofing material, do not forget about the length of the slope and the cutting of the material. With this form, there will be a lot of waste, part of it is used for the roof of the opposite side. The number of different roofing materials is determined in its own way. After all, their useful area is always less than the nominal due to overlap (roofing material, sheets of slate, corrugated board).
For complex configurations, combine the above methods for calculating the area of various geometric shapes.
You can find out the area of walls, ceiling, floor, entire room or roof of common configurations using a tape measure, pencil and calculator. For calculations, one, at most three, formulas known from high school are usually sufficient. To accurately determine the building materials, you should work with each of them separately. Materials should be taken with a margin.After all, they will be cut, cut, some will go to waste, and the percentage of marriage is not excluded.
When buying roofing materials, do not forget about the length of the slope - how much the roof will protrude beyond the walls, and the useful area of the material. Roofing material, sheets of tiles, slate always overlap each other.