## 2D Shapes

## What are 2D Shapes?

**Two-dimensional (2D) shapes are flat figures that have only length and width, but no depth.**They exist solely on a plane, meaning they are confined to two dimensions and do not have any thickness. These shapes can be geometrically defined by points, lines, curves, and angles that form closed boundaries.

## Names of 2D Shapes

**Circle****Triangle****Square****Rectangle****Rhombus****Parallelogram****Trapezoid (US)/Trapezium (UK)****Pentagon****Hexagon****Octagon****Ellipse (Oval)**

## Types of 2D Shapes

Two-dimensional (2D) shapes can be categorized into regular and irregular shapes based on the equality of their sides and angles:

### Regular 2D Shapes

- All sides are equal in length, and all interior angles are equal.
**Examples:**Square (all four sides and angles are equal), equilateral triangle (all three sides and angles are equal).

### Irregular 2D Shapes

- The sides and angles are not equal.
**Examples:**Scalene triangle (no sides or angles are the same), rectangle (opposite sides are equal, but all sides are not the same length).

## Properties of 2D Shapes

### 1. Circle

A circle is a perfectly round shape characterized by all points on the perimeter being equidistant from a single point in the center. Circles are unique among 2D shapes in having no straight edges or vertices. They are known for their infinite lines of symmetry.

**Edges and Vertices:**A circle has no edges or vertices.**Symmetry:**Highly symmetrical, with an infinite number of lines of symmetry passing through the center.

### 2. Triangle

A triangle is a polygon with three edges and three vertices. It’s the simplest polygon and can be classified based on side length (equilateral, isosceles, scalene) and angle (acute, obtuse, right). Each type of triangle has its own unique properties and uses.

**Edges and Vertices:**Consists of three edges and three vertices.**Types:**Can be categorized as equilateral, isosceles, or scalene based on side lengths; and acute, right, or obtuse based on angle sizes.

### 3. Square

A square is a regular quadrilateral with all four sides equal in length and all four angles at 90 degrees. It has four lines of symmetry and rotational symmetry of 90 degrees. Squares are often used in design and tiling due to their simplicity and symmetry.

**Edges and Vertices:**Four edges of equal length and four vertices.**Symmetry:**Four lines of symmetry and rotational symmetry of 90 degrees.

### 4. Rectangle

A rectangle is a quadrilateral with opposite sides equal in length and all angles at 90 degrees. It has two lines of symmetry. Rectangles are commonly used in everyday life, from architectural designs to everyday objects.

**Edges and Vertices:**Four edges with opposite sides equal in length and four vertices.**Symmetry:**Two lines of symmetry and rotational symmetry of 180 degrees.

### 5. Rhombus

A rhombus is a four-sided polygon with all sides of equal length, differing from the square in the angle of the corners, which are not 90 degrees.

**Edges and Vertices:**Four edges of equal length and four vertices.**Symmetry:**Two lines of diagonal symmetry.

### 6. Parallelogram

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The opposite angles are also equal. Parallelograms do not usually have lines of symmetry but have rotational symmetry.

**Edges and Vertices:**Four edges with opposite sides equal and parallel, and four vertices.**Symmetry:**No lines of symmetry (in most cases).

### 7. Trapezoid (US)/Trapezium (UK)

A trapezoid (US) or trapezium (UK) is a quadrilateral with at least one pair of parallel sides. In the US, a trapezoid has exactly one pair of parallel sides, while in the UK, it has at least one pair. This shape is commonly used in truss structures and bridges.

**Edges and Vertices:**Four edges with at least one pair of parallel sides, and four vertices.**Symmetry:**May have one line of symmetry if it is an isosceles trapezoid.

### 8. Pentagon

A pentagon is a five-sided polygon that can be regular (all sides and angles equal) or irregular. Regular pentagons have each internal angle measuring 108 degrees and exhibit rotational and reflective symmetry.

**Edges and Vertices:**Five edges and five vertices.**Symmetry:**A regular pentagon has five lines of symmetry; irregular pentagons may have none.

### 9. Hexagon

A hexagon is a six-sided polygon. In its regular form, each internal angle is 120 degrees. Regular hexagons are known for their efficiency in tiling and often appear in nature, such as in honeycomb structures.

**Edges and Vertices:**Six edges and six vertices.**Symmetry:**A regular hexagon has six lines of symmetry; irregular hexagons may have fewer or none.

### 10. Octagon

An octagon is an eight-sided polygon that can also be regular or irregular. A regular octagon has each angle at 135 degrees. Stop signs are often shaped as regular octagons.

**Edges and Vertices:**Eight edges and eight vertices.**Symmetry:**A regular octagon has eight lines of symmetry; irregular octagons may have fewer or none.

### 11. Ellipse (Oval)

An ellipse, or an oval, is a curve on a plane that surrounds two focal points. The sum of the distances from any point on the ellipse to the two focal points is constant. Ellipses have two lines of symmetry, along the major and minor axes.

**Edges and Vertices:**An ellipse has a smooth, continuous curve and therefore no edges or vertices in the traditional sense.**Symmetry:**Two lines of symmetry, one along each axis (major and minor).

## Area and Perimeter of 2D Shapes

Shape | Area Formula | Perimeter Formula |
---|---|---|

Circle | πr² (where r is the radius) | 2πr |

Triangle | 1/2×base×height | Sum of all sides |

Square | s² (where s is the side length) | 4s |

Rectangle | length×width | 2× (length+width) |

Rhombus | 1/2×d₁×d₂ (where d1 and d2 are the lengths of the diagonals) | 4×side4×side |

Parallelogram | base×height | 2×(base+side) |

Trapezoid (US)/Trapezium (UK) | 1/2×(base1+base2)×height | Sum of all sides |

### Difference Between 2D and 3D Shapes

Aspect | 2D Shapes | 3D Shapes |
---|---|---|

Dimensions | Have two dimensions: length and width. | Have three dimensions: length, width, and height (or depth). |

Appearance | Flat and can only be viewed from one perspective. | Solid and can be viewed from multiple perspectives. |

Surface | Only one surface, which is the shape itself. | Multiple surfaces (faces). |

Edges | Consist of straight or curved lines with no volume. | Have edges that are lines where two surfaces meet. |

Vertices | Points where two edges meet. | Points where edges meet, often creating a corner. |

Examples | Circle, triangle, square, rectangle. | Cube, sphere, cylinder, pyramid. |

Measurement | Measured by area (e.g., square units). | Measured by volume (e.g., cubic units). |

Common Uses | Used in drawings, designs, and flat surfaces. | Used in modeling real-world objects and structures. |

## FAQs

## What are the regular 2D shapes?

Regular 2D shapes have all sides and angles equal. Examples include equilateral triangles, squares, and regular pentagons.

## What is a 1000000000000000 sided shape called?

A shape with 1,000,000,000,000,000 sides is called a “chiliagon,” generally used to describe any polygon with a very high number of sides.

## What is the most popular 2D shape?

The circle is often considered the most popular 2D shape due to its perfect symmetry and extensive use in various fields, including mathematics and design.