Geometric Formulas and Shapes: 2D and 3D

This page presents a comprehensive collection of geometric formulas and visual representations for both two-dimensional and three-dimensional shapes. The information is organized into distinct sections for easy reference.

The first section focuses on wzory na pola figur (formulas for areas of shapes) in 2D geometry. It includes formulas for:

• Square: P = a²
• Rectangle: P = a · b
• Triangle: P = (a · h) / 2

Vocabulary: P represents the area, a and b are side lengths, and h is the height.

The next section covers more complex 2D shapes:

• Right-angled triangle
• Equilateral triangle
• Rhombus
• Trapezoid
• Parallelogram
• Regular hexagon

Example: For a rhombus, two formulas are provided: P = a · h and P = (d1 · d2) / 2, where d1 and d2 are the diagonals.

The third section presents formulas for 3D solids, focusing on objętość bryły (volume of solids) and pole powierzchni bryły (surface area of solids). Key shapes include:

• Cuboid (rectangular prism): V = a · b · c, Pc = 2(ab + bc + ac)
• Cube: V = a³, Pc = 6a²
• Prism: V = Pp · H, Pc = 2Pp + Pb
• Pyramid: V = (Pp · H) / 3, Pc = Pp + Pb

Definition: V represents volume, Pc is total surface area, Pp is base area, and Pb is lateral surface area.

The final section provides visual representations of key 3D shapes:

• Prism
• Cuboid
• Cube
• Pyramid

Highlight: The document includes a legend explaining abbreviations used throughout, such as V for volume, P for area, and n for the number of sides in the base of a prism or pyramid.

This comprehensive guide serves as an excellent resource for students studying geometry, providing wzory na pola i objętości figur przestrzennych (formulas for areas and volumes of spatial figures) in a clear and concise format.