Mathematical Formulas for Geometry
This page presents a comprehensive collection of wzory matematyczne klasa 8 do druku, focusing on area formulas for 2D shapes and volume formulas for 3D solids. These formulas are crucial for students preparing for the Egzamin Ósmoklasisty 2024.
Area Formulas (Pola Figur)
The document begins with area formulas for various 2D shapes, which are essential wzory na egzamin ósmoklasisty PDF. These include:
- Square (Kwadrat): P = a²
- Rectangle (Prostokąt): P = a · b
- Triangle (Trójkąt): P = (a · h) / 2
- Parallelogram (Równoległobok): P = a · h
- Trapezoid (Trapez): P = [(a + b) · h] / 2
- Regular Hexagon (Sześciokąt foremny): P = (3a² · √3) / 2
Highlight: The area formula for a regular hexagon is particularly important as it's less commonly memorized but often appears in advanced geometry problems.
Volume Formulas (Bryły)
The page also includes volume formulas for 3D solids, which are part of the wszystkie wzory matematyczne klasa 8 i 7:
- Cube (Sześcian): V = a³
- Cuboid (Prostopadłościan): V = a · b · c
- Pyramid (Ostrosłup): V = (Pp · H) / 3, where Pp is the area of the base and H is the height
Definition: Pp in the pyramid volume formula refers to "pole podstawy" or the area of the base of the pyramid.
Additional Formulas
The document concludes with two additional important formulas:
- Pythagorean Theorem: A² + B² = C²
Example: This theorem is used to calculate the length of the hypotenuse in a right-angled triangle when the lengths of the other two sides are known.
- Diagonal of a Regular Hexagon: d = a√3
Vocabulary: In this formula, 'd' represents the diagonal length, and 'a' is the length of one side of the hexagon.
These formulas collectively form a crucial set of wzory na Egzamin Ósmoklasisty 2024, covering key concepts in geometry that students are expected to master for their exams.
