Shapes are a fundamental part of geometry, which is the branch of mathematics that deals with the study of spatial relationships. In this lesson, we will explore the basic concepts of shapes, their properties, and how they are classified.

What are Shapes?

A shape is a two-dimensional figure that can be defined by its perimeter or boundary. Shapes are flat and have no depth. They can be made up of straight or curved lines and can have different properties such as sides, angles, and vertices.

Types of Shapes Shapes can be classified into two main categories: 2D shapes and 3D shapes.

2D shapes are flat shapes that have only length and width. They are also known as plane shapes or geometric figures. Some examples of 2D shapes are triangles, rectangles, squares, circles, and polygons.

3D shapes, on the other hand, have length, width, and height or depth. They are also known as solid shapes. Some examples of 3D shapes are cubes, spheres, cones, pyramids, and cylinders.

Properties of Shapes Shapes have different properties that make them unique.

Some of the most common properties of shapes are:

Sides – The straight lines that make up a shape.

Vertices – The points where two or more sides of a shape meet.

Angles – The degree of turn between two intersecting lines.

Diagonals – The line segments that connect two non-adjacent vertices of a shape.

Perimeter – The total distance around the boundary of a shape.

Area – The amount of space inside a shape.

Classification of Shapes Shapes can also be classified based on their properties.

Some of the most common classifications of shapes are:

Regular Shapes – Shapes that have all sides and angles equal, such as squares and circles.

Irregular Shapes – Shapes that have sides and angles of different lengths and sizes, such as polygons.

Convex Shapes – Shapes that have all angles less than 180 degrees and all diagonals that are inside the shape, such as triangles and pentagons.

Concave Shapes – Shapes that have at least one angle greater than 180 degrees and at least one diagonal that is outside the shape, such as stars and crescents.

Practice Exercise Now that you have learned about the different types of shapes and their properties, let’s try a practice exercise.

Identify the following shapes and their properties:

  1. Square
  2. Triangle
  3. Rectangle
  4. Circle
  5. Trapezoid
  6. Cube
  7. Sphere
  8. Pyramid


  1. Regular 2D shape with 4 equal sides and angles
  2. 2D shape with 3 sides and 3 angles that add up to 180 degrees
  3. 2D shape with 4 sides and 4 angles, opposite sides are equal in length
  4. 2D shape with no corners or vertices, all points are equidistant from the center
  5. 4-sided 2D shape with one pair of parallel sides
  6. 3D shape with 6 square faces and 12 edges
  7. 3D shape with a curved surface and no corners or edges
  8. 3D shape with a polygonal base and triangular sides that meet at a common vertex


Shapes are essential in mathematics and are used in various fields such as engineering, architecture, and art. By understanding the different types of shapes, their properties, and how they are classified, you can improve your problem-solving and visualization skills. Remember to always identify the shape’s properties when solving geometry problems.

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