# Area of ​​a geometric figure: what it is, concept and calculation examples

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:

1. 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.

2. 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.

3. 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.

4. 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:

• 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 .

• 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.

• 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.

• 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.

• 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.

• 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.

Below are some of the most relevant applications:

• 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.
Author:
Publication Date: October 10, 2023
Last Revision: October 10, 2023