The concept of area is fundamental in geometry, a branch of mathematics dedicated to the study of shapes and spatial properties. The area of a geometric figure is a measure that allows us to quantify the extension of a surface in the plane or in three-dimensional space.
Understanding what area is and how to calculate it is essential in a variety of fields, from construction and architecture to physics and engineering.
What is the area?
Area is a measurement that tells us how much space a geometric figure occupies on a plane or in three-dimensional space. In other words, area allows us to answer the question: "How much space is inside this shape?" Area is expressed in square units, such as square meters (m²) or square centimeters (cm²), depending on the unit system being used.
The area is an intrinsic property of a geometric figure and does not depend on its position or orientation in the plane or in space. For example, the area of a square with sides 5 cm is always 25 cm², no matter how the square is rotated or moved.
Calculation of the area of basic geometric figures
The calculation of the area of basic geometric figures is based on specific formulas for each type of figure. Here are some of the most common formulas:
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Area of the rectangle: The area of a rectangle is calculated by multiplying the length of its base (b) by its height (h). The formula is: A = b * h.
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Triangle Area: The area of a triangle is calculated by multiplying the length of the base (b) by the height (h) and dividing the result by 2. The formula is: A = (b * h) / 2.
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Area of Circle: The area of a circle is calculated using the formula A = π * r², where π (pi) is a constant approximately equal to 3.14159 and r is the radius of the circle.
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Area of Square: The area of a square is calculated by squaring the length of one of its sides. The formula is: A = L², where L is the length of one side of the square.
These are just some of the basic formulas for calculating the area of simple geometric figures. However, there are more complex formulas for more complicated figures, such as the area of a trapezoid, the area of a parallelogram, among others.
The area in geometric bodies
The calculation of areas in geometric bodies is an extension of the concept of area that is applied to three-dimensional figures instead of plane figures. The area of a geometric body corresponds to the sum of the areas of all the geometric figures that form its faces.
Below we mention some examples:
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Surface area of a cube: It is calculated by adding the area of each of its six faces. Since all faces are the same, you can use the formula: Total area of cube = 6 * (side) 2 .
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Surface area of a prism: add the area of each of the side faces and the two bases. The general formula is: total area of prism = 2 * area of base + perimeter of base * height of prism.
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Surface area of a pyramid: It is calculated by adding the area of the base and the area of the side faces. The general formula is: total area of the pyramid = area of the base + 0.5 * perimeter of the base * apothem of the pyramid.
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Surface area of a cylinder: add the area of the two circular bases and the area of the lateral surface. The formula is: total area of cylinder = 2 * area of base + circumference of base * height of cylinder.
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Surface area of a sphere: The surface area of a sphere is calculated using the formula: area of sphere = 4π * (radius) 2 , where "radius" is the radius of the sphere and π (pi) is a constant approximately equal to 3.14159.
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Surface Area of a Cone: The total surface area of a cone is calculated by adding the area of the circular base and the area of the lateral surface. The formula is: total area of the cone = area of the base + π * radius * generatrix, where the "generatrix" is the length of a segment connecting the vertex of the cone to the edge of the base.
Applications of the area in everyday life
The concept of area has significant applications in a variety of fields and situations in everyday life.
- In construction and architecture, calculating area is essential to determining the amount of materials needed to build a structure.
- In agriculture, area calculation is used to determine the amount of arable land available on a plot of land, which helps farmers plan crop planting and estimate agricultural production.
- Civil engineers use the area to design roads, bridges and other infrastructure and calculate the amount of land to excavate or fill in a construction project.
- In cartography, area is used to measure and represent the Earth's surface on maps.
- In the natural sciences, area is used to measure the surface area of ecosystems, such as forests, lakes, and oceans.
- In physics, the calculation of area can be relevant to determine the net force exerted on an object or to analyze the distribution of electric charges on a surface.