Shapes: Definition, Types, Properties and Examples

A shape is the form or outline of an object. Shapes help us describe the appearance of objects based on their boundaries, sides, angles, and dimensions. In geometry, shapes are classified into two-dimensional (2D) and three-dimensional (3D) forms.

Table of Contents

• What are Shapes?
• Types of Shapes
• Properties of Shapes
• Applications of Shapes
• Common Shapes Around Us
• Area of a Shape
• Perimeter of a Shape
• Volume of Shapes
• Sample Problems
• Frequently Asked Questions on Shapes

What are Shapes?

A shape is the form or outline of an object. Shapes help us describe objects based on their boundaries, sides, angles, and dimensions. In geometry, shapes are broadly classified into two categories: two-dimensional (2D) shapes and three-dimensional (3D) shapes.

Types of Shapes

Geometrical shapes are broadly classified into two major categories - 2D and 3D shapes. We use geometry concepts to work with various 2D as well as 3D shapes like triangles, circles, squares, cubes, cones, etc. The properties of all these geometrical shapes are based on the basic geometrical concepts of line, point, angles, and planes.

 

2-D Shapes

 

3D Shapes

 

Properties of Shapes

Every shape has certain characteristics that help us identify and classify it. These characteristics are known as the properties of shapes. Some common properties include the number of sides, vertices (corners), and angles. Understanding these properties makes it easier to recognize different geometrical shapes and compare them.

Applications of Shapes

Shapes have many applications in real life. The foundation of a house is usually rectangular in shape; by finding the perimeter of the foundation, we can calculate the cost of raising a proper foundation for the house. By finding the area of a rectangular plot, we can estimate the floor area and cost of material used for construction. Gardening is another such example where area and perimeter will help us plant flowerpots all across the perimeter of a garden. Knowing the perimeter & area of a square lawn will help to plant flowerpots all across the perimeter of the lawn and understand the quantity of seeds required to cover the whole lawn. To understand more about the topic and its application, download the area and perimeter of shapes worksheets.

Common Shapes Around Us

Shapes can be seen everywhere in our daily lives. From the objects we use at home to the buildings and roads around us, geometrical shapes help us understand and describe the world. Recognizing shapes in everyday objects makes learning geometry more meaningful and practical.

Observing shapes in everyday objects helps students connect geometry with real-life situations. It also improves visual recognition skills and builds a strong foundation for understanding more advanced geometry concepts.

Area of a Shape

The area of a shape is the space enclosed within its boundary. It tells us how much space is occupied by any shape and is usually calculated in square units like square centimetres or square metres. We can use formulas to measure the area of rectangular boxes, square playgrounds, circular pools, and so many other objects using the different formulas of area.

For example, to calculate the area of a rectangular plot, we use the formula Area = Length X Breadth.

Perimeter of a Shape

The perimeter of a shape is the total length of the boundary of a shape. In other words, it is the distance covered along the border of a closed shape. To calculate the perimeter of a shape, we have to add the length of each side. It is measured in linear units like centimetres, meters, or inches. The perimeter of a curved shape like a circle is called a circumference. The formula to calculate the perimeter of a rectangle is Perimeter = 2(Length + Breadth).

Volume of Shapes

The volume of a 3D shape is the amount of space it occupies and is measured in cubic units. Various mathematical formulas are used to find the storage capacity of cylindrical tanks, packaging cost for cubical boxes, etc.

Sample Problems

Sample Problem 1: Find the area and perimeter of a square with side = 6 cm.

Solution:

Formula for area of a square: Area = side × side.
Substitute: Area = 6 × 6 = 36.
Area = 36 cm².

Formula for perimeter of a square: Perimeter = 4 × side.
Substitute: Perimeter = 4 × 6 = 24.
Perimeter = 24 cm.

Answer: Area = 36 cm², Perimeter = 24 cm.

Sample Problem 2: Find the area and perimeter of a rectangle with length = 10 cm and width = 4 cm.

Solution:

Area formula: Area = length × width.
Substitute: Area = 10 × 4 = 40.
Area = 40 cm².

Perimeter formula: Perimeter = 2 × (length + width).
First add: length + width = 10 + 4 = 14.
Then multiply: Perimeter = 2 × 14 = 28.
Perimeter = 28 cm.

Answer: Area = 40 cm², Perimeter = 28 cm.

Sample Problem 3: A right triangle has legs 6 cm and 8 cm. Find its area and perimeter.

Solution:

Area formula for triangle: Area = (1/2) × base × height.
Take base = 6 cm and height = 8 cm (they are the two legs).
Area = 1/2 × 6 × 8 = 0.5 × 48 = 24.
Area = 24 cm².

For perimeter, first find the hypotenuse using Pythagoras (because it’s a right triangle):
Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10.
Perimeter = 6 + 8 + 10 = 24.
Perimeter = 24 cm.

Answer: Area = 24 cm², Perimeter = 24 cm.

Sample Problem 4: Find the circumference and area of a circle with radius r = 5 cm. Use π = 3.14.

Solution:

Circumference formula: C = 2 × π × r.
C = 2 × 3.14 × 5.
Compute 2 × 5 = 10 → So C = 10 × 3.14
Circumference = 31.4 cm.

Area formula: Area = π × r².
r² = 5 × 5 = 25.
Area = 3.14 × 25.
Area = 78.05 cm².

Answer: Circumference = 31.4 cm, Area = 78.05 cm².

Frequently Asked Questions on Shapes

1. What are the different types of shapes?

Answer: Two-dimensional shapes are square, rectangle, triangle, circle, and parallelogram. Three-dimensional shapes are cylinders, cones, cubes, and cuboids.

2. Why are shapes important in geometry?

Answer: Shapes help us describe, measure, and understand objects around us. They form the foundation of geometry and are used in architecture, engineering, design, construction, and everyday life.

These can work well as FAQ/PAA-style answers on your Shapes page.

3. What are the 20 types of shapes?

Answer: The 20 common types of shapes include:

1. Circle

2. Triangle

3. Square

4. Rectangle

5. Parallelogram

6. Rhombus

7. Trapezium

8. Kite

9. Pentagon

10. Hexagon

11. Heptagon

12. Octagon

13. Nonagon

14. Decagon

15. Ellipse

16. Cube

17. Cuboid

18. Cylinder

19. Cone

20. Sphere

These shapes can be broadly classified into two categories: 2D shapes and 3D shapes.

4. What are the 12 types of shapes?

Answer: The 12 most common geometric shapes are:

1. Circle

2. Triangle

3. Square

4. Rectangle

5. Parallelogram

6. Rhombus

7. Trapezium

8. Pentagon

9. Hexagon

10. Octagon

11. Cube

12. Sphere

These shapes are widely used in geometry to study sides, angles, area, perimeter, and volume.

5. What are the 10 basic shapes?

Answer: The 10 basic shapes commonly taught in geometry are:

1. Circle

2. Triangle

3. Square

4. Rectangle

5. Oval

6. Pentagon

7. Hexagon

8. Octagon

9. Cube

10. Sphere

These basic shapes help students understand geometric concepts and identify objects in everyday life.

6. What are 30 shapes?

Answer: Thirty common geometric shapes are:

1. Circle

2. Triangle

3. Square

4. Rectangle

5. Parallelogram

6. Rhombus

7. Trapezium

8. Kite

9. Pentagon

10. Hexagon

11. Heptagon

12. Octagon

13. Nonagon

14. Decagon

15. Hendecagon

16. Dodecagon

17. Ellipse

18. Semicircle

19. Sector

20. Annulus

21. Cube

22. Cuboid

23. Sphere

24. Cylinder

25. Cone

26. Prism

27. Pyramid

28. Hemisphere

29. Tetrahedron

30. Torus

These shapes include both plane (2D) shapes and solid (3D) shapes used in geometry and real-world applications.