3D Geometric Shapes and Their Formulas

This page focuses on three-dimensional shapes, providing essential formulas for the egzamin ósmoklasisty 2024. The wzory na e8 presented here include formulas for cubes, cuboids (rectangular prisms), and triangular prisms.

For cubes, the formulas cover surface area (P = 6a²), volume (V = a³), and diagonal length (D = a√3). The edge length of a cube is represented by 'a'.

Cuboid formulas are more complex, including surface area (P = 2(ab + bc + ac)), volume (V = abc), and diagonal length (D = √(a² + b² + c²)). The dimensions of a cuboid are represented by a, b, and c.

Triangular prism formulas are provided for both regular and irregular prisms. For regular triangular prisms, the perimeter is given by Obw = 3(2a + H), where 'a' is the side length of the triangular base and 'H' is the height of the prism. The surface area formula is P = 2Pp + Pb, where Pp is the area of the triangular base and Pb is the lateral surface area. The volume is calculated as V = Pp · H.

Vocabulary: Pp refers to the area of the base (podstawa) of a prism, while Pb represents the lateral surface area (pole boczne).

Example: For a cube with side length 4 cm, the volume would be V = 4³ = 64 cm³, and the surface area would be P = 6 · 4² = 96 cm².

Definition: The diagonal of a cuboid (D) is the longest line segment that can be drawn inside the shape, connecting opposite corners.

Highlight: Understanding the relationship between surface area and volume is crucial for solving complex geometry problems in the egzamin ósmoklasisty.