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 = ((a + b) • h)/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.