# What Are Geometric Shapes? Types & Examples

*Understanding geometric shapes is a pivotal aspect of mathematics. In this article, we will explore the world of geometric shapes, focusing on their types, properties, and examples.*

Understanding geometric shapes is a pivotal aspect of mathematics. Geometric shapes are everywhere, from the natural world to human-made structures. There are various ways to classify them based on specific rules and characteristics. In this article, we will explore the world of geometric shapes, focusing on their types, properties, and examples.

## Introduction to Geometric Shapes

Geometric shapes are the forms and figures that define our world. They can be classified based on dimensions into two main categories: two-dimensional (2D) shapes, which are flat and lie on a plane, and three-dimensional (3D) shapes, which have depth in addition to length and width. Some shapes are beyond our 3D perception and do not fall under the above categories. These shapes are either purely theoretical or exist in higher dimensions, and they are often explored and understood through mathematical concepts rather than physical experience. A prime example of such a shape is the tesseract, also known as a hypercube.

## Key features of Geometric Shapes

Shapes can be distinguished from one another by their key features. These features include:

- Edges/Sides – These structures are used to define boundaries in shapes. They can be either lines or curves.
- Faces – The surfaces that are bound by edges are known as faces. Closed 2D shapes are faces themselves, and 3D shapes are composed of several faces.
- Vertices – The points where two or more edges meet are called vertices.
- Angles – The space created at a vertex/corner is called an angle. The size of an angle is usually measured in degrees.

## Open and Closed Shapes

All geometric shapes can be categorized into the following two groups:

**Open shapes** – Shapes that do not enclose a region. They have lines or curves that do not connect completely. Examples of open shapes include simple line segments, arcs, or any figures that do not form an uninterrupted path.

**Closed shapes** – Shapes that form a complete loop and enclose a region. Examples of closed shapes are circles, squares, triangles, and polygons. Unlike open shapes, closed shapes can contain an area or volume.

## Examples of 2D Shapes

**Circles**: Defined by a set of points that are equidistant from a center point, circles have a single curved edge and no vertices.**Triangles**: These three-sided polygons vary based on side lengths and angles. Types include equilateral, isosceles, scalene, and right-angled triangles.**Quadrilaterals**: Including squares, rectangles, parallelograms, trapezoids, and rhombuses, these four-sided polygons have different properties based on side lengths and angles.**Polygons with More than Four Sides**: Pentagons (five sides), hexagons (six sides), heptagons (seven sides), and more, with regular forms having equal sides and angles.

## Examples of 3D Shapes

**Spheres**: Round 3D objects with all points on the surface equidistant from the center.**Cubes**: Six-faced 3D shapes with square faces. A cube has 12 vertices and 8 straight edges. 6-sided dice,**Cylinders**: A shape with two flat circular faces and a curved surface. Cylinders have no vertices. Real-life examples of cylinders include food tins, cans, and paper rolls.**Cones**: Shapes with a circular base tapering to a point.**Pyramids**: Polyhedrons with a base that can be any polygon and triangular faces meeting at a point.**Prisms:**A prism is a polyhedron with identical bases that are connected by rectangular or parallelogram faces. All prisms have an axis perpendicular to its base along which its cross-section remains uniform. The shape of the bases defines the type of prism, such as triangular, rectangular, or hexagonal.

The above list includes some of the basic 2D and 3D shapes, but there are infinitely many shapes that can be formed using line segments, curves, and other fundamental geometric objects. On top of that, composite shapes can be created by combining one or more of the basic shapes mentioned previously.

## Classifications Based on Regularity

**Regular Shapes**: These shapes have sides that are all of equal length and angles of equal measure. Examples include regular polygons like equilateral triangles and squares.**Irregular Shapes**: Shapes that do not have equal side lengths and angles. An example is a scalene triangle.

## Classifications Based on Symmetry

Symmetry is a key characteristic of geometric shapes. A shape is considered symmetric if it can be split along a line, known as the line of symmetry, in such a way that the resulting halves are mirror images of one another. Certain shapes, such as scalene triangles, lack any lines of symmetry (Note that some irregular shapes have lines of symmetry). In contrast, shapes like squares, equilateral triangles, and isosceles triangles possess a finite number of symmetry lines. Distinctively, a circle stands out as it has an infinite number of lines of symmetry, any of which pass through its center.

## Types of Faces: Curved and Flat

**Curved Shapes**: Shapes like spheres and cylinders have curved surfaces without edges or vertices.**Flat Shapes**: These are shapes with flat surfaces, like cubes and pyramids, which have flat faces, edges, and vertices.

### Geometry in Real Life

Geometric shapes are integral to various fields and activities. Architects use geometric principles to design structures; engineers employ them in machinery and vehicle construction. In nature, geometric shapes are seen in the formation of crystals, the structure of cells, and the design of honeycombs.

## Conclusion

Geometric shapes are not just academic concepts; they are essential to understanding and interacting with the world. From the simplest circle to the most complex polyhedron, these shapes help us make sense of our surroundings and contribute to advancements in science, technology, and everyday life. By exploring and understanding different types of geometric shapes, students gain a deeper appreciation of the world’s structure and the mathematical principles that underpin it.