24 November 2023

In mathematics, the surface area of ​​a figure refers to the total area that cover all their faces. It is an important concept in many different branches of mathematics, including geometry and calculus.

The calculation of surface area plays an important role in several divisions of mathematics, both in physics and engineering, where it is used to define properties such as friction force and heat transfer. In the following article we will be able to determine the characteristics of geometric figures and understand a little more about this topic.

## Definition of surface in mathematics

In mathematics, the surface is a measure of the extension of an object in two dimensions. It is defined as the set of points in space that satisfy a certain equation and must be represented graphically by means of parametric curves.

A surface can be flat or curved, depending on the number of dimensions in the space in which it lies. That is why there are different types of surfaces according to its shape and its qualities in geometry.

The theory of surfaces also has important implications in areas of concern to physics and engineering. In differential geometry, surfaces are studied as mathematical objects in themselves. Tools are used to analyze its properties. The curvature of a surface is a measure of how much it curves at each point and can be positive, negative, or zero.

Topology, on the other hand, focuses on properties that do not change under continuous deformations, such as the number of holes or connectivity. These tools are essential for understand the shape and structure of surfacesand have applications in fields such as theoretical physics and cosmology.

## In what unit of measure is an area measured?

In the construction industry, the most common measure used to calculate an area is he (m²). The square meter is a unit of area that is defined as the area of ​​a square whose sides measure one meter each.

In some cases, other units of measurement such as square feet (ft²) may be used, especially in the United States and United Kingdom. However, the use of the square meter It is used by most countries around the world due to its simplicity and clarity.

It is important to note that at talk about uneven or curved surfaces, the measurement is made using specialized techniques that allow obtaining precise results. In addition, there may be other measures used to assess the performance or quality of a specific surface.

Likewise, there are measures that are used in different areas. For example, in the construction uses the cubic meter (m³) in measuring volumes of materials such as concrete or earth.

In the textile industry, the linear meter (m) is used to measure the length of fabrics and fabrics. In cooking, proportions such as the tablespoon, cup, or gram are used to calculate ingredients. Is important to know the units of measure appropriate in each situation, since this will allow us to make precise measurements and avoid errors in our calculations.

## What types of surface are there?

Generally speaking, there are various types of surfaces in the world. Between them, we can mention solid surfaces, which are easy to identify due to their consistency and hardness.

On the other hand, we also find liquid surfaces, which appear in a fluid state and can take the shape of the container that contains them. Likewise, there are gaseous surfaces, which are those made up of molecules They move freely in a certain space. Finally, there are more complex surfaces such as human skin or the earth’s crust.

In conclusion, knowledge of the different types of surface It is important to understand our environment and how it affects physical phenomena. In addition to the types of surface mentioned, there are other qualities that manage to define a surface, such as its texture, color or temperature.

The texture is smooth, rough, rough or irregular, which can affect the way we interact with it. Color can also influence shape. in which we perceive a surface, since it manages to be attractive or repulsive to the eye.

The temperature of a surface is hot or cold, which reaches to affect our comfort when playing it. In general, the study of surfaces is important in understanding how we interact with the environment and how we can manipulate and control the properties of surfaces to achieve certain goals.

## What is the difference between the surface area and the area of ​​a figure?

Surface and area are two different but related concepts in geometry. While surface area refers to the measurement of the outside of an object, area indicates the amount of space inside the object. For example, if we take a plane figure in a rectangle, its surface is equal to the sum of the squareswhile its area gives the result of multiplying its base by its height.

In other words, we can say that surface area is a two-dimensional measure that describes an object from above, while area is a single two-dimensional measure. Therefore, although both terms related to size and shape of any geometric figure, each one has a particular use and application within the field of mathematics. The difference between them is important, to understand concepts such as volume, density and perimeter in various disciplines.

The surface of geometric figures plays a fundamental role in the study and understanding of mathematical concepts. The triangle, for example, is a figure that can have different shapes and sizes, but its surface allows us to determine its area and compare it with other figures. Similarly, the segment, although it does not have a surface itself, its length provides us with important information in various geometric calculations.

In the case of the trapezoid, its surface allows us to calculate the area of ​​this four-sided figure, which is essential for problems related to construction or geometry. Finally, the circumference, a curved figure Formed by all points equidistant from a center, its surface allows us to calculate the area of ​​a circle, being a fundamental concept in geometry and in many practical applications, such as engineering or physics.

The meaning of the area of ​​a surface it is important in many aspects of life and understanding it is essential for success in a variety of fields. Therefore, mastering this concept requires deep learning of mathematical formulas and their applications in various disciplines.