Fundamental Geometric Formulas and Theorems
This page introduces crucial geometric concepts and formulas, focusing on áreas y perímetros de figuras geométricas and fundamental theorems.
The Pythagorean theorem is presented, showing the relationship between the sides of a right triangle. The formula h² = c² + c² is given, where h represents the hypotenuse and c the catheti.
Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
Thales' theorem is also introduced, though not explicitly defined on this page.
Highlight: Understanding these theorems is crucial for solving more complex geometric problems and is often used in ejercicios resueltos de áreas y perímetros.
The page then provides a comprehensive list of fórmulas de figuras geométricas área y perímetro, including:
- Square: Perimeter = sum of sides, Area = l²
- Rectangle: Perimeter = sum of sides, Area = b * h
- Triangle: Perimeter = sum of sides, Area = (b * h) / 2
- Rhomboid: Perimeter = sum of sides, Area = b * h
- Rhombus: Perimeter = sum of sides, Area = (D * d) / 2
- Trapezoid: Perimeter = sum of sides, Area = ((B + b) * h) / 2
- Circle: Circumference = 2πr, Area = πr²
- Regular Polygon: Perimeter = sum of sides, Area = (P * a) / 2
Vocabulary: Apothem (a) is the distance from the center of a regular polygon to the midpoint of any side.
The page also includes a diagram showing how to calculate the length of a circle's arc using the formula L = (2πr * α) / 360°, where α represents the central angle in degrees.
Example: To calculate the área de un polígono regular, multiply the perimeter by the apothem and divide by 2. For instance, if a hexagon has a perimeter of 24 cm and an apothem of 3.46 cm, its area would be (24 * 3.46) / 2 = 41.52 cm².
