• Written By Vaibhav_Raj_Asthana
  • Last Modified 15-03-2024

Geometry: Definition, Shapes, Structure, Examples


Geometry is a branch of mathematics that is largely concerned with the forms and sizes of objects, their relative positions, and the qualities of space. The word Geometry is derived from the Ancient Greek word were geo- “earth,” -metron “measuring”. Euclid, the Greek mathematician who is known as the “Father of Geometry,” developed a number of postulates and theorems.

Geometry is a discipline of mathematics that connects distances, angles, patterns, areas, and volumes using mathematical concepts. Geometry is the general concept for all visually and spatially related topics. On this page, let’s take a look at all of the major themes in Geometry. Read further to find more.

Geometry: 2D And 3D Shapes

2d shapes are plane figures that can be drawn on a piece of paper. Some examples of 2d figures are given below:

Geometry 2d Shapes

3d shapes are those which can be represented in 3d space and can be solid as well as hollow. Some 3d figures are given below:

Geometry 3d shapes

What Is Plane Geometry?

Plane Geometry involves those shapes and figures that can be drawn on a piece of paper just like 2d figures. It is also referred to as 2d geometry wherein calculations are based on the length and breadth of the figures. Circle, rhombus, square are examples of plane geometry.


A point or a dot is a location or a place on a plane that is dimensionless, sizeless and only has a position. There can be single or multiple points in a plane.


The figure below shows a line. It has no end points and extends to infinity towards both the ends.

Geometry Line


Ray is a type of line which has one fixed point and extends to infinity towards the other. XY is the ray in the below figure.

Line, Line Segment, Ray, Point

Line Segment

A line segment is a type of line that has fixed points and is not infinite on either end.

Geometry Line Segment

Angles In Geometry

Angles are formed when two rays emerge from a common point. An angle can vary from 0° to 360°. Various shapes form various angles; for example, all the angles in a square and rectangle are 90°.

Angles are of 5 types:

  • i) Acute Angle
  • ii) Obtuse Angle
  • iii) Right Angle
  • iv) Straight Angle
Geometry Acute Angle
Geometry Obtuse Angle
Geometry Right Angle
Geometry Straight Angle

Polygons In Geometry

Closed figures formed by line segments which are represented in a plane are called Polygons. These figures have a minimum of 3 lines (sides) and can have n number of maximum lines. The point where two lines join to form an angle is called a vertex.

Types Of Polygons

  • i) Triangles
  • ii) Quadrilaterals
  • iii) Pentagon
  • iv) Hexagon
  • v) Heptagon
  • vi) Octagon
  • vii) Nonagon
  • viii) Decagon
Geometry Polygons
Polygons with angles

Coordinate Plane: X-Axis And Y-Axis

A plane formed when two lines intersect each other at right angles (90°) is called a coordinate plane. This is usually used to draw bar graphs, charts, etc.

Geometry Axis

The point where two axis intersect is called origin (0,0). Any point on the X-axis line will have 0 value of y (a,0) and any point on Y axis will have 0 value of x (0,y).

X and Y Plane in Geometry

If the point lies above X and Y axis the it will have both the values and will be represented as given in the above image A(25,25).

Edges, Faces, & Vertices In Geometry

Below we have tabulated some facts on the number of edges, the number of faces as well as the number of vertices in various geometrical figures.

Edges In Geometry

ShapeNumber of Edges
Triangular Prism9
Rectangular prism12
Pentagonal Prism15
Hexagonal Prism18
Triangular Pyramid6
Square Pyramid8
Pentagonal Pyramid10
Hexagonal Pyramid12

Practice 12th CBSE Exam Questions

Vertices In Geometry

ShapesNumber of Vertices
Triangular Prism6
Rectangular prism8
Pentagonal Prism10
Hexagonal Prism12
Triangular Pyramid4
Square Pyramid5
Pentagonal Pyramid6
Hexagonal Pyramid7

Faces In Geometry

ShapesNumber of Faces
Triangular Prism5
Rectangular prism6
Pentagonal Prism7
Hexagonal Prism8
Triangular Pyramid4
Square Pyramid5
Pentagonal Pyramid6
Hexagonal Pyramid7

Geometry Symbols

Below we have provided some basic symbols that are used in geometry to represent objects or things.

SymbolSymbol Name
Right angle
° or degDegree
Double prime
ABLine segment
Congruent to
c or rad radians
g or grad gradians / gons

Geometry Formulas

In thsi section, we have provided the basic geometry formulas that will aid you in preparing for the topic. We will use the following abbreviations for convenience:

  • 1. LSA – Lateral/Curved Surface Area
  • 2. TSA – Total Surface Area
Name of the Solid FigureFormulas
CuboidLSA: 2h(l + b)
TSA: 2(lb + bh + hl)
Volume: l × b × h

l = length,
b = breadth,
h = height
CubeLSA: 4a2
TSA: 6a2
Volume: a3

a = sides of a cube
Right PyramidLSA: ½ × p × l
TSA: LSA + Area of the base
Volume: ⅓ × Area of the base × h

p = perimeter of the base,
l = slant height, h = height
Right Circular CylinderLSA: 2(π × r × h)
TSA: 2πr (r + h)
Volume: π × r2 × h

r = radius,
h = height
Right Circular ConeLSA: πrl
TSA: π × r × (r + l)
Volume: ⅓ × (πr2h)

r = radius,
l = slant height,
h = height
Right PrismLSA: p × h
Volume: B × h

p = perimeter of the base,
B = area of base, h = height
SphereLSA: 4 × π × r2
TSA: 4 × π × r2
Volume: 4/3 × (πr3)

r = radius
HemisphereLSA: 2 × π × r2
TSA: 3 × π × r2
Volume: ⅔ × (πr3)

r = radius

Also, check other study resources from Embibe:

Maths Formulas For Class 8Maths Formulas For Class 10
Trigonometry TableTrigonometric Ratios
Mensuration FormulasAlgebra Formulas


Geometry is a branch of mathematics concerned with the forms, angles, dimensions, and sizes of a wide range of objects seen in daily life. Geometry is derived from two Ancient Greek words: ‘geo’ which means ‘Earth,’ and ‘metron’ which means ‘measurement.’ There are two-dimensional and three-dimensional forms in Euclidean geometry.

Flat shapes are 2d shapes such as triangles, squares, rectangles, and circles in plane geometry. Solids are 3D forms such as a cube, cuboids, cones, and others in solid geometry. Coordinate geometry explains how points, lines, and planes are used in fundamental geometry.

Geometry’s many forms of shapes help us in understanding the shapes we encounter in daily life. We can compute the area, perimeter, and volume of forms using geometric ideas.

Frequently Asked Questions: FAQs

Here are some questions that are mostly searched on the topic:

Q. What are the basics of geometry?
Basics of any topic refer to the general concepts and theories that are necessary for understanding concepts. In this case, it involves angles, vertices, plane, line, line segment, shapes, etc.
Q. Is high school geometry hard?
A topic or a subject can be hard or easy depending upon how you understand it. If you have all the resources, the formulas are at your fingertips, and your concepts are clear, things become really easy in geometry. All you need to do is clear your basic concepts.
Q. What is geometry?
The word geometry has been derived from the Greek word “Geo” and “Metry”. Geo means earth and Metry means measurement.
Q. What are all the Geometry applications?
Geometry has a wide range of applications from ancient times till now and will be valid in future as well. All constructions are done using geometrical concepts, data evaluation, projection of things, navigation, MRI, etc.

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