We know geometric figures as shapes or structures defined in mathematics that could be represented on a plane or in space. These can be circles, squares, rectangles or cones and are studied in geometry.
In general, these figures are usually of two or three dimensions and have properties that define them, such as length, area, volume, angles, symmetry, among others. Throughout this article we will talk specifically about what the area of a geometric figure is, what it is for and how it is determined.
Concept and meaning of area in mathematics
In mathematics, the area is known as the measure of extension of a geometric figure located in the plane or space. Likewise, area is understood as the magnitude used to quantify how much space a figure tends to occupy on a defined surface.
Thus, the area is considered one of the most fundamental properties of geometric figures. In this sense, the determination of it is of the utmost importance in different branches of mathematics, such as trigonometry, geometry and calculus.
On the other hand, the calculation of the area of a geometric figure It can be very useful in solving practical problems in areas such as physics, engineering, architecture, construction, etc.
What is the use of knowing the area of a geometric figure?
The determining the area of a geometric figure It is very helpful in various practical applications, some of the most common uses of area calculation are:
- construction and architecture: The ascription of the area of geometric figures is important for the design and construction of buildings. In general, it is used to calculate the amount of materials needed to make a structure or to determine the cost of the work.
- Engineering: when designing and building from machines, tools or devices that require parts with specific shapes and precise sizes, the calculation of the area is of the utmost importance. With it you can calculate the size of the piece to be made more precisely, reducing design errors.
- physics and mechanics: Calculating area is valuable in determining the force to be exerted on a surface. In addition, it also helps define the work done in moving an object or the amount of energy needed to do a task.
- Geometry: the calculation of the area is considered essential when studying the properties of geometric figures. In the same way, these figures are used to determine the characteristics, such as angles, symmetry, diagonals and the relationships between their parts.
- Daily life: This tool can be very helpful to do different simple tasks, such as calculating the size of a piece of land, painting a room, or even choosing a rug for a certain space.
In general, it is known for being a important tool in various areas of study as well as in the daily life of humans.
How is the area of a geometric figure determined?
The way in which the area of any geometric figure can be determined It will depend on its shape and characteristics.. In the same way, below, we will describe the formulas to calculate the area of the most common geometric figures:
- area of a rectangle: Rectangles have four sides, of which two are equal and parallel to each other and the other two too, but perpendicular to the first.
To calculate the area (A) of a rectangle we just have to multiply its base by its height. The base is understood as one of the parallel sides of the rectangle, while the height is the perpendicular distance between the two parallel sides, and the formula is as follows: W = base x height
- area of a triangle: A triangle is a type of polygon that has three sides and three angles. The sum of the interior angles of a triangle must always equal 180 degrees.
When calculating the area of a triangle, you must know the length of its base and its height. The base is one of the sides of said figure and the distance is the perpendicular from the base to the opposite vertex, likewise, the formula to calculate the area of the triangle is: A = (base x height) / 2
- area of a square: Squares are geometric figures that have four equal sides and four right angles, that is, 90 degrees.
Calculating the area of a square is very simple and you only have to know the length of one of its sides. The formula to calculate it is as follows: A = side x side = side²
- area of a circle: Circles are curved geometric figures where all points on their perimeter are at the same distance from the center. The measure of this distance is known as the radius.
When you want to calculate the area of a circle, you need to know the length of its radius. Thus, the formula would look like this: A = π x radius²where “π” (Pi= 3.1416, approximately) is a constant value.
Formula to find the area of geometric figures
In addition to the geometric figures described in the previous point, there are many more, which have their own formula for calculate its areathey are between them:
- Trapeze: A = ((major base + minor base) / 2) x height
- Diamond: A = (major diagonal x minor diagonal) / 2
- Parallelogram: W = base x height
- regular hexagon: A = (3√3 x side²) / 2
- regular pentagon: A = (perimeter x apothem) / 2
- regular octagon: A = 2(1 + √2) x side²
In general, if a complex geometric figure is presented, this can be divided into segments or parts that are easier to calculate and specific formulas would be used for each segment. This type of calculation tries to find a formula where the dimensions of the figure can be related to its area.