Geometric Formulas for 2D and 3D Shapes

This page presents a comprehensive collection of wzory na pola figur (formulas for figure areas) and other geometric calculations for various shapes. The formulas are organized neatly with accompanying diagrams, making it an excellent resource for students studying pola i obwody figur płaskich (areas and perimeters of plane figures) as well as three-dimensional solids.

The page begins with formulas for two-dimensional shapes. For the square (kwadrat), it provides formulas for area $P = a²$, perimeter $L = 4a$, and diagonal $d = a√2$. The rectangle (prostokąt) follows with area $P = a·b$ and perimeter $L = 2a + 2b$ formulas. The parallelogram (równoległobok) and trapezoid (trapez) are also included with their respective area and perimeter formulas.

Vocabulary: Kwadrat - Square, Prostokąt - Rectangle, Równoległobok - Parallelogram, Trapez - Trapezoid

For the rhombus (romb), the area formula using diagonals $P = (d₁·d₂)/2$ is provided along with the perimeter formula. The triangle (trójkąt) section is particularly detailed, offering formulas for area using base and height $P = (a·h)/2$ and perimeter $L = a + b + c$.

Highlight: Special attention is given to the right triangle (trójkąt prostokątny), including a diagram of a 30-60-90 triangle with side length relationships.

The page then transitions to three-dimensional shapes. It includes formulas for pyramids (ostrosłup), cubes (sześcian), and rectangular prisms (prostopadłościan). For each of these solids, formulas for surface area (Pc) and volume (V) are provided.

Example: For a cube with side length a, the surface area is given by Pc = 6a², and the volume by V = a³.

The document concludes with formulas for general prisms (graniastosłup), showing how to calculate surface area and volume using the area of the base (Pp) and height (H).

This comprehensive guide serves as an excellent reference for students studying geometry, particularly those preparing for exams like the egzamin ósmoklasisty. The clear layout and visual representations make it easy to quickly find and apply the needed formulas for various geometric calculations.