Quadrilaterals and Circle

This page expands on wzory na pola figur by covering more complex quadrilaterals and introducing the circle.

The rhombus is presented first, with its perimeter formula (4 times the side length) and area formula (side length times height).

Definition: A rhombus is a quadrilateral with four equal sides, but angles that are not necessarily right angles.

The circle follows, introducing π (pi) in the formulas. The circumference is calculated as 2πr, where r is the radius, and the area is πr².

Highlight: The value of π is approximately 3.14159, but in calculations, it's often rounded to 3.14 or represented by the symbol π.

The isosceles trapezoid is then shown, with a perimeter formula summing all sides and an area formula using the average of parallel sides multiplied by height.

Vocabulary: An isosceles trapezoid is a trapezoid where the non-parallel sides are of equal length.

The rectangle is presented next, with its perimeter formula as twice the sum of length and width, and area as length times width.

Example: For a rectangle with length 8 cm and width 5 cm, the perimeter would be 2$8+5$ = 26 cm, and the area would be 8 * 5 = 40 cm².

Lastly, the kite is introduced, with its perimeter as the sum of two pairs of equal sides and area as half the product of its diagonals.

Definition: A kite is a quadrilateral with two pairs of adjacent sides of equal length.

Parallelogram

This final page focuses on the parallelogram, another important shape in the study of wzory na pola i obwody figur.

The parallelogram is presented with its perimeter and area formulas. The perimeter is calculated as twice the sum of its base and side lengths: L = 2$a+b$.

Definition: A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

The area of a parallelogram is given by the product of its base and height: P = a * h. This formula is similar to that of a rectangle, but uses the perpendicular height rather than the side length.

Highlight: The area formula for a parallelogram demonstrates that its area is equivalent to that of a rectangle with the same base and height.

Example: For a parallelogram with base 6 cm, side 4 cm, and height 5 cm, the perimeter would be 2$6+4$ = 20 cm, and the area would be 6 * 5 = 30 cm².

This page completes the comprehensive guide to wzory figur geometrycznych, providing students with a valuable resource for calculating perimeters and areas of various plane figures.

Triangles and Square

This page introduces formulas for different types of triangles and squares, essential for understanding pola i obwody figur płaskich.

The equilateral triangle is presented first, with formulas for its perimeter and area. The perimeter is calculated as 3 times the side length, while the area uses the side length and height.

Definition: An equilateral triangle is a triangle with all sides of equal length and all angles measuring 60 degrees.

Next, the right-angled triangle is shown, with formulas for perimeter (sum of all sides) and area (half the product of base and height).

Highlight: The formula for the area of a right-angled triangle, P = 1/2 * a * h, is a special case of the general triangle area formula.

The scalene triangle follows, with similar formulas but emphasizing that all sides can have different lengths.

Vocabulary: A scalene triangle is a triangle where all three sides have different lengths.

Lastly, the square is presented with its perimeter formula (4 times the side length) and area formula (side length squared).

Example: For a square with side length 5 cm, the perimeter would be 4 * 5 = 20 cm, and the area would be 5² = 25 cm².