Geometric Formulas for 2D and 3D Shapes
This page presents a comprehensive collection of wzory na pola figur formulasforfigureareas 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 areasandperimetersofplanefigures 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 roˊwnoległobok 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 troˊjkąt 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 troˊjkątprostokątny, 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 szesˊcian, and rectangular prisms prostopadłosˊcian. 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.
