Find the area of ​​a parallelogram using the formula: S = b × h. Parallelograms are similar to rectangles with one exception - their angles are not necessarily 90 degrees. Accordingly, the calculation of the area of ​​a parallelogram is carried out in a similar way for a rectangle: the length of the base side in centimeters is multiplied by the height of the parallelogram in centimeters. Any side is taken as the base, and the height is determined by the length of the perpendicular to it from the opposite obtuse angle figures.

• For example, if the length of the base of a parallelogram is 5 cm and its height is 4 cm, its area will be: 5 x 4 = 20 square centimeters.

Calculate the area of ​​a trapezoid using the formula: S = 1/2 × h × (B+b). A trapezoid is a quadrilateral with two sides parallel to each other, and the other two are not. To determine the area of ​​a trapezoid in square centimeters, you need to know three measurements (in centimeters): the length of the longer parallel side B, the length of the shorter parallel side b and the height of the trapezoid h(defined as the shortest distance between its parallel sides along a segment perpendicular to them). Add together the lengths of the two parallel sides, divide the sum in half and multiply by the height to get the area of ​​the trapezoid in square centimeters.

• For example, if the longer of the parallel sides of the trapezoid is 6 cm, the shorter is 4 cm, and the height is 5 cm, the area of ​​\u200b\u200bthe figure will be: ½ x (6 + 4) x 5 \u003d 25 square centimeters.

Find the area of ​​a regular hexagon: S = ½ × P × a. The above formula is only valid for a regular hexagon with six equal parties and six identical corners. letter P the perimeter of the figure is indicated (or the product of the length of one side by six, which is true for a regular hexagon). letter a the length of the apothem is indicated - the distance from the center of the hexagon to the middle of one of its sides (the point located in the middle between two adjacent vertices of the figure). Multiply the perimeter and apothem in centimeters and divide the result by two to find the area of ​​a regular hexagon.

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1 square meter [m²] = 10000 square centimeter [cm²]

Initial value

Converted value

square meter square kilometer square hectometer square decameter square decimeter square centimeter square millimeter square micrometer square nanometer hectare ar barn square mile sq. mile (US survey) square yard square foot² sq. ft (US, survey) square inch circular inch township section acre acre (US, survey) ore square chain square rod² (US, survey) square perch square rod sq. thousandth circular mil homestead sabine arpan cuerda square castilian cubit varas conuqueras cuad electron cross-section tithe (official) household tithe round square verst square arshin square foot square sazhen square inch (Russian) square line Plank area

More about the area

General information

Area is the size geometric figure in two-dimensional space. It is used in mathematics, medicine, engineering, and other sciences, such as calculating the cross section of cells, atoms, or pipes such as blood vessels or water pipes. In geography, area is used to compare the sizes of cities, lakes, countries, and other geographic features. Area is also used in population density calculations. Population density is defined as the number of people per unit area.

Units

Square meters

Area is measured in SI units in square meters. One square meter is the area of ​​a square with a side of one meter.

unit square

A unit square is a square with sides of one unit. The area of ​​a unit square is also equal to unity. In a rectangular coordinate system, this square is at coordinates (0,0), (0,1), (1,0) and (1,1). On the complex plane, the coordinates are 0, 1, i and i+1, where i is an imaginary number.

Ar

Ar or sotka, as a measure of area, is used in the CIS countries, Indonesia and some other European countries, to measure small urban objects such as parks, when a hectare is too large. One ar is equal to 100 square meters. In some countries, this unit is called differently.

Hectare

Real estate is measured in hectares, especially land. One hectare is equal to 10,000 square meters. It has been in use since the French Revolution, and is used in the European Union and some other regions. As well as ar, in some countries the hectare is called differently.

Acre

AT North America and Burma area is measured in acres. Hectares are not used there. One acre is equal to 4046.86 square meters. Initially, an acre was defined as the area that a peasant with a team of two oxen could plow in one day.

barn

Barns are used in nuclear physics to measure the cross section of atoms. One barn equals 10⁻²⁸ square meters. Barn is not a unit in the SI system, but is accepted for use in this system. One bar approx. equal to area cross-section of the uranium nucleus, which physicists jokingly called "huge as a barn." Barn in English "barn" (pronounced barn) and from a joke of physicists, this word became the name of a unit of area. This unit originated during World War II, and was liked by scientists because its name could be used as a code in correspondence and telephone conversations within the Manhattan Project.

Area calculation

The area of ​​the simplest geometric figures is found by comparing them with the square of a known area. This is convenient because the area of ​​a square is easy to calculate. Some formulas for calculating the area of ​​​​geometric shapes below are obtained in this way. Also, to calculate the area, especially a polygon, the figure is divided into triangles, the area of ​​\u200b\u200beach triangle is calculated using the formula, and then added. The area of ​​more complex figures is calculated using mathematical analysis.

Area formulas

• Square: square side.
• Rectangle: product of the parties.
• Triangle (side and height are known): the product of a side and the height (the distance from that side to the edge) divided in half. Formula: A = ½ah, where A- square, a- side, and h- height.
• Triangle (two sides and the angle between them are known): the product of the sides and the sine of the angle between them, divided in half. Formula: A = ½ab sin(α), where A- square, a and b are the sides, and α is the angle between them.
• Equilateral triangle: side, squared, divided by 4 times Square root out of three.
• Parallelogram: the product of a side and the height measured from that side to the opposite side.
• Trapeze: the sum of two parallel sides multiplied by the height, divided by two. Height is measured between these two sides.
• A circle: the product of the square of the radius and π.
• Ellipse: product of semiaxes and π.

Surface area calculation

You can find the surface area of ​​simple three-dimensional figures, such as prisms, by unfolding this figure on a plane. It is impossible to obtain a ball scan in this way. The surface area of ​​a sphere is found using the formula by multiplying the square of the radius by 4π. From this formula it follows that the area of ​​a circle is four times less area surface of a sphere with the same radius.

Surface areas of some astronomical objects: Sun - 6.088 x 10¹² square kilometers; Earth - 5.1 x 10⁸; thus, the surface area of ​​the Earth is about 12 times smaller than the surface area of ​​the Sun. The surface area of ​​the Moon is approximately 3.793 x 10⁷ square kilometers, which is about 13 times smaller than the surface area of ​​the Earth.

planimeter

The area can also be calculated using a special device - a planimeter. There are several types of this device, for example, polar and linear. Also, planimeters are analog and digital. In addition to other features, digital planimeters can be scaled to make it easier to measure features on a map. The planimeter measures the distance traveled along the perimeter of the measured object, as well as the direction. The distance traveled by the planimeter parallel to its axis is not measured. These devices are used in medicine, biology, engineering, and agriculture.

Area properties theorem

According to the isoperimetric theorem, of all figures with the same perimeter, the most big square at the circle. If, on the contrary, we compare figures with the same area, then the circle has the smallest perimeter. The perimeter is the sum of the lengths of the sides of a geometric figure, or a line that marks the boundaries of this figure.

Geographic features with the largest area

Country: Russia, 17,098,242 square kilometers, including land and water. The second and third largest countries are Canada and China.

City: New York is a city with the most large area in 8683 square kilometers. The second largest city is Tokyo, covering 6,993 square kilometers. The third is Chicago, with an area of ​​5498 square kilometers.

City Square: The largest area, covering 1 square kilometer, is located in the capital of Indonesia, Jakarta. This is Medan Merdeka Square. The second largest area at 0.57 square kilometers is Praça dos Giraçois in the city of Palmas, in Brazil. The third largest is Tiananmen Square in China, 0.44 square kilometers.

Lake: Geographers argue whether the Caspian Sea is a lake, but if it is, then it is the largest lake in the world with an area of ​​371,000 square kilometers. The second largest lake is Lake Superior in North America. It is one of the lakes of the Great Lakes system; its area is 82,414 square kilometers. The third largest is Lake Victoria in Africa. It covers an area of ​​69,485 square kilometers.

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1 square centimeter [cm²] = 0.0001 square meter [m²]

Initial value

Converted value

square meter square kilometer square hectometer square decameter square decimeter square centimeter square millimeter square micrometer square nanometer hectare ar barn square mile sq. mile (US survey) square yard square foot² sq. ft (US, survey) square inch circular inch township section acre acre (US, survey) ore square chain square rod² (US, survey) square perch square rod sq. thousandth circular mil homestead sabine arpan cuerda square castilian cubit varas conuqueras cuad electron cross-section tithe (official) household tithe round square verst square arshin square foot square sazhen square inch (Russian) square line Plank area

Electric field strength

More about the area

General information

Area is the size of a geometric figure in two-dimensional space. It is used in mathematics, medicine, engineering, and other sciences, such as calculating the cross section of cells, atoms, or pipes such as blood vessels or water pipes. In geography, area is used to compare the sizes of cities, lakes, countries, and other geographic features. Area is also used in population density calculations. Population density is defined as the number of people per unit area.

Units

Square meters

Area is measured in SI units in square meters. One square meter is the area of ​​a square with a side of one meter.

unit square

A unit square is a square with sides of one unit. The area of ​​a unit square is also equal to unity. In a rectangular coordinate system, this square is at coordinates (0,0), (0,1), (1,0) and (1,1). On the complex plane, the coordinates are 0, 1, i and i+1, where i is an imaginary number.

Ar

Ar or sotka, as a measure of area, is used in the CIS countries, Indonesia and some other European countries, to measure small urban objects such as parks, when a hectare is too large. One are is equal to 100 square meters. In some countries, this unit is called differently.

Hectare

Real estate is measured in hectares, especially land plots. One hectare is equal to 10,000 square meters. It has been in use since the French Revolution, and is used in the European Union and some other regions. As well as ar, in some countries the hectare is called differently.

Acre

In North America and Burma, area is measured in acres. Hectares are not used there. One acre is equal to 4046.86 square meters. Initially, an acre was defined as the area that a peasant with a team of two oxen could plow in one day.

barn

Barns are used in nuclear physics to measure the cross section of atoms. One barn equals 10⁻²⁸ square meters. Barn is not a unit in the SI system, but is accepted for use in this system. One barn is approximately equal to the cross-sectional area of ​​the uranium nucleus, which physicists jokingly called "huge as a barn." Barn in English "barn" (pronounced barn) and from a joke of physicists, this word became the name of a unit of area. This unit originated during World War II, and scientists liked it because its name could be used as a code in correspondence and telephone conversations within the Manhattan Project.

Area calculation

The area of ​​the simplest geometric figures is found by comparing them with the square of a known area. This is convenient because the area of ​​a square is easy to calculate. Some formulas for calculating the area of ​​​​geometric shapes below are obtained in this way. Also, to calculate the area, especially a polygon, the figure is divided into triangles, the area of ​​\u200b\u200beach triangle is calculated using the formula, and then added. The area of ​​more complex figures is calculated using mathematical analysis.

Area formulas

• Square: square side.
• Rectangle: product of the parties.
• Triangle (side and height are known): the product of a side and the height (the distance from that side to the edge) divided in half. Formula: A = ½ah, where A- square, a- side, and h- height.
• Triangle (two sides and the angle between them are known): the product of the sides and the sine of the angle between them, divided in half. Formula: A = ½ab sin(α), where A- square, a and b are the sides, and α is the angle between them.
• Equilateral triangle: side, squared, divided by 4 times the square root of three.
• Parallelogram: the product of a side and the height measured from that side to the opposite side.
• Trapeze: the sum of two parallel sides multiplied by the height, divided by two. Height is measured between these two sides.
• A circle: the product of the square of the radius and π.
• Ellipse: product of semiaxes and π.

Surface area calculation

You can find the surface area of ​​simple three-dimensional figures, such as prisms, by unfolding this figure on a plane. It is impossible to obtain a ball scan in this way. The surface area of ​​a sphere is found using the formula by multiplying the square of the radius by 4π. From this formula it follows that the area of ​​a circle is four times less than the surface area of ​​a ball with the same radius.

Surface areas of some astronomical objects: Sun - 6.088 x 10¹² square kilometers; Earth - 5.1 x 10⁸; thus, the surface area of ​​the Earth is about 12 times smaller than the surface area of ​​the Sun. The surface area of ​​the Moon is approximately 3.793 x 10⁷ square kilometers, which is about 13 times smaller than the surface area of ​​the Earth.

planimeter

The area can also be calculated using a special device - a planimeter. There are several types of this device, for example, polar and linear. Also, planimeters are analog and digital. In addition to other features, digital planimeters can be scaled to make it easier to measure features on a map. The planimeter measures the distance traveled along the perimeter of the measured object, as well as the direction. The distance traveled by the planimeter parallel to its axis is not measured. These devices are used in medicine, biology, engineering, and agriculture.

Area properties theorem

According to the isoperimetric theorem, of all figures with the same perimeter, the circle has the largest area. If, on the contrary, we compare figures with the same area, then the circle has the smallest perimeter. The perimeter is the sum of the lengths of the sides of a geometric figure, or a line that marks the boundaries of this figure.

Geographic features with the largest area

Country: Russia, 17,098,242 square kilometers, including land and water. The second and third largest countries are Canada and China.

City: New York is the city with the largest area at 8,683 square kilometers. The second largest city is Tokyo, covering 6,993 square kilometers. The third is Chicago, with an area of ​​5498 square kilometers.

City Square: The largest area, covering 1 square kilometer, is located in the capital of Indonesia, Jakarta. This is Medan Merdeka Square. The second largest area at 0.57 square kilometers is Praça dos Giraçois in the city of Palmas, in Brazil. The third largest is Tiananmen Square in China, 0.44 square kilometers.

Lake: Geographers argue whether the Caspian Sea is a lake, but if it is, then it is the largest lake in the world with an area of ​​371,000 square kilometers. The second largest lake is Lake Superior in North America. It is one of the lakes of the Great Lakes system; its area is 82,414 square kilometers. The third largest is Lake Victoria in Africa. It covers an area of ​​69,485 square kilometers.