# How do you calculate the area

## Contents

• 1 How to calculate the binary forms space dimensions 1.1 square space 1.2 space rectangle 1.3 Circle area 1.4 Triangle area 1.5 designated area 1.6 parallel ribs space 1.7 trapezoidal area
• 1.1 square space
• 1.2 space rectangle
• 1.3 Circle area
• 1.4 Triangle area
• 1.5 designated area
• 1.6 parallel ribs space
• 1.7 trapezoidal area
• 2 How to calculate the three-dimensional space models 2.1 roller surface area 2.2 parallel surface area of ​​rectangles 2.3 surface area of ​​the pyramid 2.4 surface area of ​​the ball 2.5 surface of the cone area 2.6 surface area of ​​the prism
• 2.1 roller surface area
• 2.2 parallel surface area of ​​rectangles
• 2.3 surface area of ​​the pyramid
• 2.4 surface area of ​​the ball
• 2.5 surface of the cone area
• 2.6 surface area of ​​the prism
• 3 curves calculate the area using integration
• 4 References

## How to calculate the binary forms space dimensions

The area known as confined within the boundaries of the geometric shape of the region; Kalmthelt, rectangle and square, circle, and other formats, it is possible to find an area of ​​any form in many ways is the simplest and most primitive way count; And be by drawing a shape on a two-dimensional graph paper (boxes), and then count the squares occupied by this form, where each square represents them square unit, and the unit is determined to be used in measuring the shape area; Kalbossh, or foot, or centimeters, or other units of measure length. [1] [2]

For Siple example, if the shape decree on this paper rectangle, and the unit used to draw squares (cm), and asked to find an area, are then simply counting the boxes inside the rectangle (assuming it 8 boxes), then type the resulting companion unit square as follows : area of ​​the rectangle = 8 cm², it can also be found space also through specific formulas and the laws of each form through which space account in a simple way, and the most prominent examples include the following: [1] [2]

### Area of ​​the square

Box is defined as a two-dimensional geometric shape, all equal in length ribs, as well as the list of the four corners and equal, [3] As for the area it is the length of the rib raised to the power of 2; Any leg length multiplied by himself; Thus: space = box (rib length) ². [4] [5] The examples that illustrate how to calculate the area of ​​the square following:

• (Example): Calculate the square space, if you know that the length of a side is equal to 20:00. [5] Solution: Using box space law, the: box area = (8) ² = 64 m².
• Solution: Using box space law, the: box area = (8) ² = 64 m².

For more information about the area of ​​the square you can read the following articles: What is the area of ​​the square, the perimeter and area of ​​the law box.

### rectangle area

Rectangle knows that the lengths of the ribs is uneven as a whole, and in which the couple Almottagablan ribs only equal, but the four corners are equal list, [6] As for the area it is a product of the length in width; Ie: rectangle area = length × width, and examples that illustrate how to calculate the area of ​​a rectangle the following: [7]

• Example: Calculate the area of ​​a rectangular card shape, if I learned that the length is equal to 5 cm, its width equals 3 cm. Solution: rectangle area = length × width = 3 × 5 = 15 cm².
• Solution: rectangle area = length × width = 3 × 5 = 15 cm².

For more information about the area of ​​the rectangle you can read the following articles: How do we calculate the rectangle area, the law of the rectangle area and perimeter.

### Circle area

Can calculate the area of ​​a circle through the use of the law as follows: area of ​​a circle = π × half Alqtr², and examples that illustrate how to calculate the area of ​​the following: [8]

• Example: Calculate the area of ​​a circle, if you know that the length of a radius equal to 4 cm. Solution: Circle area = π × half Alqtr² = 3.14 × 4² = 50.24 cm².
• Solution: Circle area = π × half Alqtr² = 3.14 × 4² = 50.24 cm².

For more information about the area of ​​a circle you can read the following articles: How to calculate the area of ​​a circle, the circle's circumference and an area of ​​the law.

### Triangle area

Can calculate the area of ​​a triangle no matter how different types through the use of the law as follows: Triangle = 1/2 space × height × length of the base, and examples that illustrate how to calculate the area of ​​the following: [8]

• Example: Calculate the area of ​​the triangle, if I learned that the length of its base is equal to 6 cm, and a height of a falling column from the opposite head of the base towards 6 cm. Solution: Triangle = 1/2 × length of the base area × height = 1/2 × 6 × 4 = 12 cm².
• Solution: Triangle = 1/2 × length of the base area × height = 1/2 × 6 × 4 = 12 cm².

For more information about the area of ​​the triangle you can read the following articles: How to Calculate the area of ​​the triangle, the perimeter and area of ​​the law of the triangle, the triangle area of ​​the law of equal legs, the triangle area of ​​equal law ribs, an area of ​​law-angled triangle.

### The designated area

Can calculate the area designated by law to use the following: designate = 1/2 × length of the first space diameter × length of the second diameter, and examples that illustrate how to calculate the area of ​​the following: [8]

• Example: Calculate the designated area, if I learned that the length of the first diameter is equal to 3 cm, and the length of the second diameter equal to 5 cm. Solution: Triangle area = 1/2 × length of the first diameter × length of the second diameter = 1/2 × 3 × 5 = 7.5 cm².
• Solution: Triangle area = 1/2 × length of the first diameter × length of the second diameter = 1/2 × 3 × 5 = 7.5 cm².

For more information about the particular area you can read the following article: the law of the designated space account.

### Parallelogram area

You can calculate the area of ​​parallel ribs by using the law as follows: parallel ribs area = length of the base × height; Where the height represents the vertical distance between the base and the corresponding rib, and examples that illustrate how to calculate the area of ​​the following: [8]

• Example: Calculate the parallel area of ​​the ribs, if I learned that the length of its base is equal to 6 cm, and a height equal to 4 cm. Solution: space parallelogram = length of the base × height = 6 × 4 = 24 cm².
• Solution: space parallelogram = length of the base × height = 6 × 4 = 24 cm².

For more information about the parallelogram space you can read the following article: space law parallelogram.

### Trapezoidal area

It can trapezoidal space is calculated by using the law as follows: trapezoidal = 1/2 space × total length × height rules; As the two bases are Dhalaan Almtoazian in trapezoidal, and the height is the vertical distance between the hyphen, and examples that illustrate how to calculate the area of ​​the following: [8]

• Example: Calculate the trapezoidal space, if you know that the length of Hadtah is equal to 6 cm, 3 cm, and a height equal to 4 cm. Solution: trapezoidal = 1/2 space × total length rules × height = 1/2 × (6 + 3) × 4 = 18 cm².
• Solution: trapezoidal = 1/2 space × total length rules × height = 1/2 × (6 + 3) × 4 = 18 cm².

For more information about the trapezoidal space you can read the following articles: semi-deviant area, trapezoidal space-based.

## How maquettes three-dimensional space calculation

Known models as a solid three-dimensional length, width, height and forms, and there are several types of models; Kalostoanh, published, and the ways to find the surface area of ​​cut-outs are done through the knowledge of the nature of geometric shapes forming the stereo, and then the area of ​​each account the face of the unit, and then complete the collection of spaces, or through the adoption of formulas and specific laws are used to find spaces in some well-known formats as It follows.

### Roller surface area

Roller is the model of a three-dimensional in which two bases Daiceka Mottagabeltan and identical, and aspects of a serpentine rectangle between the two bases, [9] and is equal to the cylinder space: the base circumference × height + 2 × the base area, and as the base one is a circle, the roller surface area = 2 × π × radius of the base × height + 2 × π × radius Alhadh², note that: circumference = 2 × π × Purify, the circle = π × Nq², space and examples that illustrate how the cylinder space calculate the following: [10]

• Example: Calculate the roller space if I learned that the radius of its base is equal to 17:00, while the height equals 19:00. Solution: roller area = (2 × π × Purify) × height + 2 × (π × Nq²) = 2 × 3.14 × 5 × 7 + 2 × 3.14 × 5² = 376 m².
• Solution: roller area = (2 × π × Purify) × height + 2 × (π × Nq²) = 2 × 3.14 × 5 × 7 + 2 × 3.14 × 5² = 376 m².

For more information about the disc space you can read the following article: an area of ​​the law of the cylinder.

### Parallel surface area of ​​rectangles

Cuboid is a publication based, contain facets of side on rectangles, in which each pair of opposite sides are identical, including two bases, and the surface area Vtsawi the base circumference × height + 2 × the base area, and as per the base is a rectangle, the: total area the cuboid = 2 × (length + PowerPoint) × height + 2 × (length × width), and from it: the total area of ​​the cuboid = 2 × (length × width) + 2 × (width × height) +2 (length × height) ; note that the perimeter of the rectangle = 2 × length + PowerPoint, and the area of ​​the rectangle = length × width, and examples that illustrate how to calculate the area cuboid the following: [11] [4]

• Example: Calculate the parallel surface area of ​​rectangles, if I learned that the length of its base 3 cm, width 4 cm, while the height equals 10 cm. Solution: surface area cuboid = 2 × (length + PowerPoint) × height + 2 × (length × width) = 2 (3 + 4) × 10 + 2 × (4 × 3) = 164 cm².
• Solution: surface area cuboid = 2 × (length + PowerPoint) × height + 2 × (length × width) = 2 (3 + 4) × 10 + 2 × (4 × 3) = 164 cm².

For more information about the parallel area of ​​rectangles you can read the following article: space law cuboid.

### The surface area of ​​the pyramid

Is the pyramid of polyhedra, containing only one rule in the form of a regular polygon, and preferential treatment side is triangles number coupled with the number of sides of the base, while calculating the surface area it is the sum of space facets triangular in addition to the base area, and therefore: [9]

• Area side of the pyramid = one area of ​​the triangle (faceted side) × number of triangles. The total surface area of ​​the pyramid = single triangle (space-faceted side) × number of triangles + the base area.
• The total surface area of ​​the pyramid = single triangle (space-faceted side) × number of triangles + the base area.

Examples that illustrate how the pyramid area account the following:

• Example: Calculate the total area of ​​the pyramid quadrant, Amaalmt that the height of the side is equal to 17 m, while the length of the rib base equals 16 m. [12] Solution: The base of this pyramid square shape, while the number of facets triangular side it (4), and it: the surface of the total pyramid area = one triangle (space-faceted side) × number of triangles + the base area = (1/2 × 16 × 17) × 4 + 16 × 16 = 800 m².
• Solution: The base of this pyramid square shape, while the number of facets triangular side it (4), therefore: total pyramid surface area = one area of ​​the triangle (faceted side) × number of triangles + the base area = (1/2 × 16 × 17) × 4 + 16 × 16 = 800 m².

For more information about the pyramid area you can read the following article: the surface of the pyramid area.

### Ball surface area

Ball represents a set of points located constant is the radius of a certain point known as ball center, can simply be the surface of the ball space account by following the law as follows: Ball area = 4 × π × half Alqtr², [9] and examples that illustrate how what area account the following: [13]

• Example: Calculate the total area of ​​the ball, Amaalmt that the radius is equal to 4 cm. Solution: Ball area = 4 × π × half Alqtr² = 4 × 3.14 × 4² = 200.96 cm².
• Solution: Ball area = 4 × π × half Alqtr² = 4 × 3.14 × 4² = 200.96 cm².

For more information about the ball space you can read the following article: ball surface area of ​​the law.

### The surface of the cone area

Cone is a pyramid base circular shape, and surface curved, and can be an area account simply by following the law as follows: cone = π area × radius of the base × (radius of the base + lateral height), [9] and examples that illustrate how an area account the following: [14]

• Example: Calculate the total area of ​​the cone, Amaalmt that the radius of its base is equal to 4 cm, and a height of 5 cm lateral. Solution: cone area = π × radius of the base × (radius of the base + height profile) = 3.14 × 4 × (4 + 5) = 113 cm².
• Solution: cone area = π × radius of the base × (radius of the base + height profile) = 3.14 × 4 × (4 + 5) = 113 cm².

For more information about the cone area you can read the following article: CONE space law.

### Prism surface area

Regular publication is based stereoscopic three-dimensional represent both identical and parallel Hadtah regular polygon shape; A triangle may be, or square, or a rectangle, or other, but preferential treatment side it is rectangular, but for an area account are through all the bases space with side-faceted space, through the law, the following: Publication area = 2 × Al Qaeda Area + perimeter of the base × prism height, and examples that illustrate how to calculate the area of ​​the following: [15]

• Example: Calculate the total area of ​​publication, Amaalmt that its base trapezoidal shape is equal to the length of Hadtah 6 cm, 12 cm, and a height of 4 cm, and the length of his legs Almtsawitin is a 5 cm, 10 cm high prism. Solution: space prism = 2 × Al Qaeda Area + perimeter of the base × height prism = 2 × 1/2 × (6 + 12) × 4 + (5 + 5 + 6 + 12) × 10 = 352 cm².
• Solution: space prism = 2 × Al Qaeda Area + perimeter of the base × height prism = 2 × 1/2 × (6 + 12) × 4 + (5 + 5 + 6 + 12) × 10 = 352 cm².

For more information about the publication space you can read the following article: four-wheel surface of the prism space.

## Calculate curves space using integration

Method of calculating the different areas of limited space within a straight cut; Kalmthelt, rectangle, and square, and other shapes for the method of calculating the area under the curves, or confined, including space, where depends athletes on the integration account in a region confined between the X-axis and curve coupling what, for example, there are more than one case for it; Sometimes a curve (or pairing, which is the mathematical formula of the curve) the beginning and end of Mallomtan and Mahddtan, therefore it is easy to get space here, which is only calculates the integration of the pairing, but some cases may need to be more complex, such as the division of the steps of the curve (pairing) to more part of, then the integration account for each section, and the collection of output in the end, and many other cases. [16]

## References

• ^ أ ب "?What is Area", www.mathsisfun.com, Retrieved 18-12-2017. Edited.
• ^ أ ب "Area: Definition & Counting Method", www.study.com, Retrieved 17-12-2017. Edited.
• ↑ "Square (Geometry)", www.mathsisfun.com, Retrieved 6-5-2020. Edited.
• ^ A b Rajai Samih al-Assar, Jawad Younis Abu Halil, Mohammed Zuhair Abu Sabih (2013), the entrance to the Olympics and math competitions (first edition), Riyadh: King Fahd University of Petroleum and Minerals Deanship Search Alalma_ Obeikan Library, page 85-90, The first part. Adapted.
• ^ أ ب "How to Find Perimeter from Area", www.study.com, Retrieved 28-11-2017. Edited.
• ↑ Known Samhan, Najla Altwaijri, Lian Tuban (2016), Mathematics Olympiad: Engineering (First Edition), Riyadh: King Abdul Aziz Foundation for talent and creativity, Obeikan, page 155-180, the first part. Adapted.
• ↑ "Area of Plane Shapes", www.mathsisfun.com, Retrieved 6-5-2020. Edited.
• ^ أ ب ت ث ج "Area Of 2 D Shapes - Definition with Examples", www.splashlearn.com, Retrieved 6-5-2020. Edited.
• ^ A b T w Rajai Samih al-Assar, Jawad Younis Abu Halil, Mohammed Zuhair Abu Sabih (2013), the entrance to the Olympic Games and the competitions of mathematics (first edition), Riyadh: King Fahd University of Petroleum and Minerals Deanship Search Alalma_ Obeikan Library, page 80. 90, the first part. Adapted.
• ↑ "Surface Area of a Cylinder", www.varsitytutors.com, Retrieved 6-5-2020. Edited.
• ↑ "Cuboid", www.mathworld.wolfram.com, Retrieved 9-12-2017. Edited.
• ↑ "Surface Area of a Pyramid", www.varsitytutors.com, Retrieved 6-5-2020. Edited.
• ↑ "Surface Area of a Sphere", www.onlinemathlearning.com, Retrieved 6-5-2020. Edited.
• ↑ "Area Of Shapes", byjus.com, Retrieved 6-5-2020. Edited.
• ↑ "Surface Area of a Prism", www.varsitytutors.com, Retrieved 6-5-2020. Edited.
• ↑ "Finding areas by integration", www.mathcentre.ac.uk, Retrieved 16/1/2017. Edited.

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