Geometrical Shapes: Check Different Shapes and Properties - Embibe
  • Written By Srotaswini Mohapatra
  • Last Modified 24-06-2022
  • Written By Srotaswini Mohapatra
  • Last Modified 24-06-2022

Geometrical Shapes: Check Different Shapes and Properties

Geometric Shapes: In Maths syllabus, Geometrical shapes play a vital role. Students need to be extra careful and prepare the topics and concepts with determination because these topics are important for future exams. Students need to have a better understanding for a better preparation plan and ace their examination.

Students find geometric shapes overwhelming and challenging. For that reason, this article has a series of concepts such as geometric patterns discussed for the benefit of the students. The article has provided in-depth explanations on shapes of triangles and geometric figures which will help students to ace the examination and also be well prepared for future competitive examinations. To know more, continue to read the article.

Geometrical Shapes/Patterns Definition

Geometrical shapes definition refers to two-dimensional shapes that are shapes and closed figures such as circles, squares, rectangles, rhombuses, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere, and cylinder. We observe all these shapes everywhere in different forms.

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Let us have a look at some real-life objects we used, which resemble some basic shapes.

Geometrical Shape

Geometric shapes are the shapes that represent the forms of different objects. Some figures are two-dimensional \(2\,{\rm{D}}\) and some are three-dimensional \(3\,{\rm{D}}\) shapes.\(2\,{\rm{D}}\) figures lie on only the \(x- \)axis and \(y – \)axis, but \(3\,{\rm{D}}\) shapes lie in the \(x,y – \) and \(z – \)axis. The \(z – \)axis represents the height of the object. There are different shapes defined in geometry like circle, square, rectangle, triangle etc.

To create any of these figures, start with a line, a line segment or else a curve. Depending upon the number of lines and their arrangement, we get different types of shapes and figures like a triangle (a figure in which three-line segments are connected), Pentagon (five-line segments) and so on.

The shapes in geometry can either be open or closed.

Open Shape: The figure that starts and ends at the different points to form a boundary by line segments or curves is called an open shape.

Open Shape

Closed Shape: The figure that starts and ends at the same point to form a boundary by line segments or by curves is called a closed shape.

Closed shape

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List of Geometric Shapes

Geometric shapes are classified with respect to their regularity or uniformity. A regular shape is symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic. The list of some geometric \(2\,{\rm{D}}\) shape and \(3\,{\rm{D}}\) shape are given below:

\(2\,{\rm{D}}\) Shapes:

  1. Triangle
  2. Circle
  3. Semi-circle
  4. Square
  5. Rectangle
  6. Parallelogram
  7. Rhombus
  8. Trapezium
  9. Kite
  10. Polygons (Pentagon, Hexagon, Octagon, Nonagon, Decagon etc.)

\(3\,{\rm{D}}\) Shapes:

  1. Sphere
  2. Cube
  3. Cuboid
  4. Cone
  5. Cylinder

Types and Properties of Geometric Shapes

Let’s see some of the types and properties of geometric shapes:

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Two-Dimensional Shapes

Triangle: Triangle is a polygon that is made of \(3\) sides and consists of \(3\) edges and \(3\) vertices. Also, the total measure of its internal angles equal to \({180^ \circ }\)

Circle: Circle is a plane geometrical round shape having all points are the same distance from the centre.

Semi-circle: Half of the circle is called the semi-circle.

Square: The type of quadrilateral in which all the sides are equal, and each angle measures \({90^ \circ }\) is called a square.

Rectangle: The type of quadrilateral in which opposite sides are of equal length, and each angle is a right angle is called a rectangle.

Parallelogram: A quadrilateral is called a parallelogram if both pairs of its opposite sides are parallel.

Rhombus: The type of quadrilateral having all sides equal is called a rhombus.

Trapezium: The type of quadrilateral having exactly one pair of parallel sides is called the trapezium.

Kite: A quadrilateral is called a kite if it has two pairs of equal adjacent sides but unequal opposite sides.

Polygons (Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon etc.): Polygons are made up of line segments and no curves. They are enclosed structures based on different lengths of sides and different angles.

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Three-Dimensional Shapes

Sphere: A sphere is a \(3\,{\rm{D}}\) round shape whose radius is extended to three dimensions.
Example: Globe

Cube: A cube is a \(3\,{\rm{D}}\) shape that has \(6\) faces,\(8\) vertices and \(12\) edges. All the faces of the cube are square.
Example: A Rubik’s cube

Cuboid: A cuboid is a three-dimensional solid shape having \(6\) faces,\(8\) vertices and  \(12\) edges but all the faces of the cuboid are in a rectangular shape. 
Example: A Lunchbox

Cone: A cone is a solid shape that has a circular base and narrows smoothly from the surface to the top at a point called apex or vertex. 
Example: A birthday cap

Cylinder: A cylinder is a \(3\,{\rm{D}}\) solid shape that has two parallel circular bases connected by a curved surface. It has no vertex. 
Example: Gas cylinder

Geometrical Figures Examples

Here we have discussed some of the geometrical figures:

Plane Geometrical Figure Examples

Circle: Wheel is an example of a circle in real life.

Square: Carom board is an example of a square in real life.

Triangle: One slice of pizza is an example of a triangle in real life.

Rectangle: Blackboard is an example of a rectangle in real life.

Oval: Egg is an example of an oval in real life.

Solid Geometrical Figures Example

Sphere: Football, spherical marbles, globes etc., are examples of a sphere.

Cube: Ice-cube, sugar cubes, dice etc. are examples of a cube.

Cuboid: Matchbox, books, lunch boxes etc., are examples of a cuboid.

Cone: Cone ice cream, birthday caps etc., are examples of a cone.

Cylinder: Can, pipe, gas cylinders etc., are examples of a cylinder.

Important Notes on Geometrical Shapes

  1. A point has no dimension, and a line is a one-dimensional shape. Both are the base of geometry. When two lines meet at a point, they form an angle where the point is said to be the vertex and lines are the arms. 
  2. The two-dimensional and three-dimensional shapes are formed using points, lines and angles. 
  3. The two-dimensional shapes that have \(4\) sides, like rectangles, squares, parallelograms, kites, trapezoids, etc., are called quadrilaterals.
  4. Quadrilateral shapes are four-sided closed figures made up of straight lines.
  5. Polygons are closed shapes made of straight lines. They are named according to the number of sides they have.
  6. A three-dimensional shape has length, breadth and height.

Geometric Patterns

Geometric patterns are the collection of shapes, repeating or altered to create a particular design.
Examples of geometric patterns are given below,

Geometric Patterns

Let us have a look at a pattern using some basic plane shapes. Some basic plane shapes are circles, squares, triangles, rectangles etc.

Geometric Patterns

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Solved Examples

Listed below are some solved examples on geometric shapes for your understanding:

Q.1.The figure given below is the open or closed figure?

A.1. The figure that starts and ends at the different points to form a boundary by line segments or by curves is called an open figure. As the given figure has both starting and ending points is different, and it is not continuous, it is an open figure.

Q.2. The figure given below is the open or closed figure?

A.2. The figure that starts and ends at the same point to form a boundary by line segments or by curves is called a closed figure. As the given figure has both starting and ending points is same, it is a closed figure.

Q.3. Give three real-life examples of a rectangle.
A.3. Rectangle is a plane geometrical closed shape having a total of four sides (two opposite sides are equal and parallel), four corners.
Real-life examples of a rectangle are currency notes, cell phones, book covers etc.

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Q.4. Write two examples of a cone.
A.4. Cone is a solid \(3\,{\rm{D}}\) shape. The two examples of the cone are birthday caps and cone ice cream.

Q.5.Count and write the number of circles, ovals, triangles, rectangles and squares in the picture given below.

A.5.
The number of circles is \(7\).
The number of ovals is \(6\).
The number of triangles is \(8\).
The number of rectangles is \(4\).
The number of squares is \(3\).

Summary

Geometrical shapes are everywhere. Almost everything is made up of both two-dimensional \(2\,{\rm{D}}\) and three-dimensional \(3\,{\rm{D}}\) geometrical shapes. In this article, we covered the definition of geometrical shapes, geometrical shapes used in real-life objects, types of geometrical shapes and their properties, open shapes, closed shapes, list of geometrical shapes, some notes on geometrical shapes, geometrical figure examples, geometrical shapes pattern etc.

It will help students understand geometric patterns and will help in understanding geometrical shapes, their properties, etc.

1. Triangles
2. Circles
3. Area of Rectangle
4. Rhombus
5. Types of Polygons

FAQs on Geometrical Shapes

Listed below are some FAQs on geometrical shapes:

Q1: What are the \(10\) basic shapes?
Ans: The \(10\) basic shapes are circle, oval, triangle, rhombus, square, rectangle, trapezoid, pentagon, hexagon and octagon.

Q2: What are \(3\) examples of a geometric shape?
Ans: The three examples of a geometric shape are circle, triangle and square

Q3: What are the \(4\) basic shapes?
Ans: The \(4\) basic geometric plane shapes are circle, triangle, rectangle and square.

Q4: What is the most common geometric shape?
Ans: Circle is the most common geometric shape.

Q5: Define Euler’s equation with an example?
Ans: Euler’s equation for any polyhedron is, \(F + V – E = 2\) where \(F\) is the number of faces, \(V\) is the number of vertices, and \(E\) number of Edges.
Example:
Now, \(F + V – E = 2\)
\(F = 2 – V + E\)
\(F = 2 – 6 + 12\)
\(F = 8\)
Hence, the number of faces is \(8.\)

Q6: How many sides do a pentagon has?
Ans: ‘Penta’ means ‘five’ So, a pentagon has \(5\) sides.

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