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 formulasforareasofshapes 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 volumeofsolids and pole powierzchni bryły surfaceareaofsolids. Key shapes include:
- Cuboid rectangularprism: V = a · b · c, Pc = 2ab+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 formulasforareasandvolumesofspatialfigures in a clear and concise format.
