Geometric Formulas for Eighth-Grade Exam
This page provides a comprehensive overview of geometric formulas that are crucial for the eighth-grade exam (egzamin ósmoklasisty). These formulas are essential for students preparing for their matematyka egzamin ósmoklasisty.
Square (Kwadrat)
The square is a regular quadrilateral with four equal sides and four right angles.
Definition: A square is a rectangle with four equal sides.
- Side length: a
- Diagonal: d = a√2
- Area: P = a²
- Perimeter: Obwód = 4a
Example: If a square has a side length of 5 cm, its area would be 25 cm² and its perimeter would be 20 cm.
Triangle (Trójkąt)
The page covers two specific types of triangles:
Right-angled Triangle (Trójkąt Prostokątny)
Highlight: The right-angled triangle is fundamental in trigonometry and the Pythagorean theorem.
- Hypotenuse: a√2
- Other sides: a and a
Equilateral Triangle (Trójkąt Równoboczny)
Vocabulary: An equilateral triangle has all sides equal and all angles equal to 60°.
- Side length: a
- Height: h = (a√3)/2
- Area: P = (a²√3)/4
Rectangle (Prostokąt)
The rectangle is a quadrilateral with four right angles.
- Length: a
- Width: b
- Area: P = a • b
- Perimeter: Obwód = 2a + 2b
Rhombus (Romb)
Definition: A rhombus is a quadrilateral with four equal sides.
- Side length: a
- Diagonals: d₁ and d₂
- Area: P = (d₁ • d₂)/2
- Perimeter: Obwód = 4a
Parallelogram (Równoległobok)
Vocabulary: A parallelogram is a quadrilateral with opposite sides parallel.
- Base: a
- Height: h
- Area: P = a • h
- Perimeter: Obwód = 2a + 2b
Trapezoid (Trapez)
Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides.
- Parallel sides: a and b
- Height: h
- Area: P = /2
- Perimeter: Obwód = a + b + c + d
Highlight: These formulas are essential for solving geometry problems in the egzamin ósmoklasisty z matematyki and should be memorized for quick application during the exam.
