Geometric Shapes and Formulas for Eighth Grade Math Exam

This page provides a comprehensive overview of essential geometric shapes and their corresponding formulas, crucial for the wzory na egzamin ósmoklasisty PDF. It serves as an excellent reference for wszystkie wzory matematyczne klasa 8 preparation.

The page is divided into sections, each focusing on a specific shape and its area formula. It begins with two-dimensional shapes and progresses to three-dimensional ones, concluding with the Pythagorean theorem.

Highlight: The visual representations accompanying each formula make this an invaluable resource for visual learners preparing for the kartkówka wzory matematyczne klasa 8.

1. Rectangle (Prostokąt): The formula P = a · b is provided, where 'a' and 'b' represent the length and width respectively.

2. Square (Kwadrat): Two formulas are given - P = a² and P = a · a, emphasizing that the area can be calculated by squaring the side length.

3. Parallelogram (Równoległobok): The formula P = a · h is shown, where 'h' represents the height perpendicular to the base 'a'.

4. Rhombus (Romb): Two formulas are presented - P = (d₁ · d₂) / 2 and P = a · h, where 'd₁' and 'd₂' are diagonals, and 'h' is the height.

5. Triangle (Trójkąt): The standard formula P = (a · h) / 2 is given, along with a special case for equilateral triangles where h = (a√3) / 2.

6. Trapezoid (Trapez): The formula P = $(a + b) · h$ / 2 is provided, where 'a' and 'b' are parallel sides and 'h' is the height.

Example: For a trapezoid with parallel sides of 6 cm and 10 cm, and a height of 4 cm, the area would be $(6 + 10) · 4$ / 2 = 32 cm².

7. Cuboid (Prostopadłościan): Surface area formula P = 2(ab + ac + bc) and volume formula V = a · b · c are given, where 'a', 'b', and 'c' are the dimensions.

Vocabulary: Prostopadłościan - A three-dimensional shape with six rectangular faces, also known as a rectangular prism or cuboid in English.

The page concludes with the Pythagorean theorem, a² + b² = c², which is fundamental for solving problems related to right-angled triangles in the stereometria egzamin ósmoklasisty section.

Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse $c$ is equal to the sum of squares of the other two sides (a and b).

This comprehensive guide serves as an excellent wzory matematyczne szkoła podstawowa PDF resource, covering all the essential geometric formulas needed for the eighth-grade math exam.