Geometrical Shapes: In Mathematics, Geometrical shapes are the figures which show the shapes of objects we see in our daily lives. In geometry, shapes are the forms of objects which have boundary lines, surfaces, and angles. There are different types of \(2\,{\rm{D}}\) and \(3\,{\rm{D}}\) shapes. In our everyday life, we constantly interact with different objects, which look like various shapes, from basic to abstract ones.
For example, books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape), and so on. In this article, you will learn different geometric shapes and their definition along with examples.
Table of Contents
 Geometrical Shapes Definition
 Geometric Shapes List
 Types of Geometric Shapes with Properties
 Basic Geometrical Figures Examples
 Solid Geometrical Figures Example
 Important Notes on Geometrical Shapes
 Geometric Patterns
 Solved Examples Geometrical Shapes:
 Summary
 Frequently Asked Questions (FAQ) – Geometrical Shapes
Geometrical Shapes Definition
In plane geometry, twodimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, etc. In solid geometry, the threedimensional shapes are cube, cuboid, cone, sphere, and cylinder. We can observe all these shapes in our daily existence also.
Let us have a look at some reallife objects we used, which resemble some basic shapes.
Geometrical shapes are the shapes that represent the forms of different objects. Some figures are twodimensional \(2\,{\rm{D}}\) and some are threedimensional \(3\,{\rm{D}}\) 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 threeline segments are connected), Pentagon (fiveline segments) and so on.
The shapes in geometry can be either 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.
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.
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Geometric Shapes List
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:
 Triangle
 Circle
 Semicircle
 Square
 Rectangle
 Parallelogram
 Rhombus
 Trapezium
 Kite
 Polygons (Pentagon, Hexagon, Octagon, Nonagon, Decagon etc.)
\(3\,{\rm{D}}\) Shapes:
 Sphere
 Cube
 Cuboid
 Cone
 Cylinder
Types of Geometric Shapes with Properties
Let’s see some of the geometric shapes with their properties:
TwoDimensional 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.
Semicircle: Half of the circle is called the semicircle.
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.
ThreeDimensional 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 threedimensional 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
Basic 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, globe etc., are examples of a sphere.
Cube: Icecube, sugar cubes, dice etc. are examples of a cube.
Cuboid: Matchbox, book, lunch box etc., are examples of a cuboid.
Cone: Cone ice cream, birthday cap etc., are examples of a cone.
Cylinder: Can, pipe, gas cylinders etc., are examples of a cylinder.
Important Notes on Geometrical Shapes
 A point has no dimension, and a line is a onedimensional 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 vertex and lines are the arms.
 The twodimensional and threedimensional shapes are formed using points, lines and angles.
 The twodimensional shapes that have \(4\) sides, like rectangle, square, parallelogram, kite, trapezoid, etc., are called quadrilaterals.
 Quadrilateral shapes are foursided closed figures made up of straight lines.
 Polygons are closed shapes made of straight lines. They are named according to the number of sides they have.
 A threedimensional 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,
Let us have a look at a pattern using some basic plane shapes. Some basic plane shapes are circle, square, triangle, rectangle etc.
Solved Examples Geometrical Shapes:
Q.1.The figure given below is the open or closed figure?
Ans: 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?
Ans: 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 reallife examples of a rectangle.
Ans: Rectangle is a plane geometrical closed shape having a total of four sides (two opposite sides are equal and parallel), four corners.
Reallife examples of a rectangle are currency notes, cell phones, book covers etc.
Q.4. Write two examples of a cone.
Ans: 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.
Ans:
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 twodimensional \(2\,{\rm{D}}\) and threedimensional \(3\,{\rm{D}}\) geometrical shapes. In this article, we covered the definition of geometrical shapes, geometrical shapes used in reallife 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.
Frequently Asked Questions (FAQ) – Geometrical Shapes
Q.1. What are the \(10\) basic shapes?
Ans: The \(10\) basic shapes are circle, oval, triangle, rhombus, square, rectangle, trapezoid, pentagon, hexagon and octagon.
Q.2. What are \(3\) examples of a geometric shape?
Ans: The three examples of a geometric shape are circle, triangle and square
Q.3. What are the \(4\) basic shapes?
Ans: The \(4\) basic geometric plane shapes are circle, triangle, rectangle and square.
Q.4.What is the most common geometric shape?
Ans: Circle is the most common geometric shape.
Q.5. 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 \(8.\)
Q.6. How many sides do a pentagon has?
Ans: ‘Penta’ means ‘five’ So, a pentagon has \(5\) sides.
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