Polygons and Types of Quadrilaterals

Geometry and Measures Polygons and Types of Quadrilaterals

🎬 Video Tutorial

What is a Polygon? (0:01)

A polygon is a closed, 2D shape made up of straight line segments only.

Examples of Polygons: Triangles, quadrilaterals, pentagons, hexagons, and stars are all polygons because they are closed shapes with only straight sides.

What is NOT a Polygon?

A shape is not a polygon if it does not meet all three conditions:

Not 2D: If a shape is three-dimensional (like a cube) or just a single point, it is not a polygon.
Not Closed: If the shape has gaps and does not fully enclose an area, it is not a polygon.
Not Straight: If any part of the shape is curved instead of straight, it is not a polygon.

Understanding polygons is important in geometry, as they form the basis of many mathematical concepts and real-world applications.

Common Polygons and Their Names (0:45)

Polygons are classified based on the number of their sides. Here are the names of some common polygons:

3-sided polygon → Triangle
4-sided polygon → Quadrilateral
5-sided polygon → Pentagon
6-sided polygon → Hexagon
7-sided polygon → Heptagon
8-sided polygon → Octagon
9-sided polygon → Nonagon
10-sided polygon → Decagon

Sum of Interior Angles of Polygons (Formula) (1:29)

The sum of all interior angles in a polygon depends on the number of sides. This can be calculated using the formula:

$$ \text{Sum of interior angles} = (n-2) \times 180^\circ $$

where $ n $ is the number of sides.

Examples:

Triangle (3 sides): $ \ (3-2) \times 180^\circ = 180^\circ $
Quadrilateral (4 sides): $ \ (4-2) \times 180^\circ = 360^\circ $
Pentagon (5 sides): $ \ (5-2) \times 180^\circ = 540^\circ $
Hexagon (6 sides): $ \ (6-2) \times 180^\circ = 720^\circ $

Understanding this formula helps in geometry when calculating unknown interior angles in polygons.

Special Types of Quadrilaterals (2:00)

A quadrilateral is a four-sided polygon. There are different types of quadrilaterals, each with unique properties:

Trapezium: Has at least one pair of parallel sides.
Parallelogram: Both pairs of opposite sides are parallel.
Rhombus: All sides are of equal length.
Rectangle: Has four right angles.
Square: All sides are equal, and all angles are right angles.

Understanding these quadrilaterals helps in geometry, construction, and design.

📂 Revision Cards

Illustrating polygons as 2D closed shapes with straight line segments, showing a triangle and star, and non-polygons like curved shape and 3D cube. — 1) Polygons vs Non-polygons

Table showing polygons with their corresponding number of sides. — 2) Regular Polygons Names

Table showing polygons, their number of sides, and sum of interior angles. Triangle (180°), quadrilateral (360°), pentagon (540°), and hexagon (720°). — 3) Interior Angles of Polygons

Illustrating special types of quadrilaterals, highlighting their unique properties such as parallel sides and equal angles. — 4) Special Quadrilaterals

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