Geometric Shapes in Maths

Geometric Shapes: Geometric shapes are the figures used in mathematics to represent the forms of real-world things. Shapes are the forms of things in geometry that have boundaries, angles, and surfaces.

There are two types of geometric figures:

• 2D Shapes(Two-dimensional)
• 3D Shapes(Three-dimensional)

Shapes are also divided into two types based on their regularity or uniformity.

• Regular Shapes– Symmetric shapes such as squares, circles, etc.
• Irregular Shapes– Asymmetric shapes or freeform shapes.

List of Geometric Shapes

Name	Type	Edges	Vertices	Faces
Square	2D	4	4	—
Rectangle	2D	4	4	—
Triangle	2D	3	3	—
Circle	2D	Curved	0	—
Pentagon	2D	5	5	—
Hexagon	2D	6	6	—
Cube	3D	12	8	6
Cuboid	3D	12	8	6
Cone	3D	1	1	2
Cylinder	3D	2	0	3
Sphere	3D	Curved	0	1

Types and Properties of Geometric Shapes

Geometric shapes are vital in understanding the world around us and play a crucial role in various disciplines, from art to engineering. Here’s an overview of the main types of geometric shapes and their properties:

2D Shapes

Name	Figure	Definition
Square		A square is a 2D figure consisting of 4 equal sides and equal angles, where each angle is equal to 90°.
Rectangle		A rectangle is a 2D figure with 4 sides where opposite sides are equal and each angle is equal to 90°.
Triangle		A triangle is a 2D figure enclosed with 3 sides and consists of 3 edges and 3 vertices and has the sum of its 3 angles equal to 180.
Circle		A circle is a closed 2D figure round in shape with no sides and corners.
Oval		An oval is also a closed 2D figure somewhat similar to a circle with elongated to some extent. It does not have
Parallelogram		A parallelogram is a quadrilateral with two pairs of parallel sides and equal opposite angles.
Trapezium		A Trapezium is a quadrilateral in which one pair of opposite sides is parallel.
Rhombus		Rhombus is a type of quadrilateral.It is a special parallelogram that has 4 equal sides and its diagonals bisect at 90.
Kite		Kite is a quadrilateral that has two pairs of equal adjacent sides.

Types of Polygons

Shapes	Figures
Triangle
Quadrilateral
Pentagon
Hexagon
Septagon
Octagon
Nonagon
Decagon

3D Shapes

Names of  3D geometric shapes	Figure	Definition
Cube		A cube is a three-dimensional shape that has 6 faces, 8 vertices, and 12 edges. The faces of the cube are square. Example: A Rubik’s cube
Cuboid		A cuboid is a three-dimensional solid having 6 rectangular faces, 8 vertices, and 12 edges.  Example: Matchbox
Cone		A cone is a solid which has a circular base and a pointed edge at the top called the apex or vertex.  Example: An ice cream cone
Cylinder		A cylinder is a 3d solid shape that has two parallel circular bases connected by a curved surface. It has no vertex.  Example: Gas cylinder
Sphere		A sphere is a round shape in a 3d plane, looking like a ball. Its radius extends in three dimensions (x-axis, y-axis, z-axis). Example: Ball

List and Properties of Geometric Shapes

The list of geometric shapes along with their edges, vertices, and faces is given below.

Open and Closed Figures

Closed Shapes

Basic geometric shapes like squares, rectangles, and triangles are a few 2D shapes. These figures are referred such as polygons. Any flat form or plane on a piece of paper is a polygon. They have finite closed boundaries made up of line segments known as sides of the polygon. Geometric figures such as polygons are known as closed figures. The boundary of a closed figure could be either made up of line segments or curves. Therefore, any geometric object that begins and ends at the same location and forms a border using line segments or curves is considered to be a closed figure.

Open Shapes

Open shapes aren’t complete. The beginning point and finishing point must be met in order to draw a closed figure. Using line segments or curves to represent open figures is another option, but at least the lines will be broken up. The origin and destination of an open figure are distinct.

Open Figures

Applications of Geometric Shapes

• Mathematics: Understanding properties of shapes helps in the study of geometry, including calculations for area, volume, and other dimensional analyses.
• Engineering and Architecture: Shapes are the foundation of design and construction, influencing the strength, aesthetics, and functionality of structures.
• Art and Design: Artists and designers use geometric shapes to create visual interest and structure in their works.

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Summary – Geometric Shapes

Geometric shapes are fundamental elements in the study of geometry, classified primarily into two-dimensional (2D) and three-dimensional (3D) shapes. 2D shapes, like circles, triangles, squares, rectangles, and polygons, are flat and defined by properties such as edges and vertices. They exist solely in terms of length and width. Common properties include the number of edges (straight lines that form the boundary), vertices (corners where edges meet), and internal angles (the angles within the shape).

3D shapes, such as spheres, cubes, cylinders, cones, and pyramids, extend into space by adding depth to the length and width, creating a third dimension. These shapes are characterized by their faces (flat or curved surfaces), edges (where two faces meet), and vertices (where multiple edges converge). Each type of shape has unique properties that dictate its volume and surface area, important for various applications in physics, engineering, and architecture.

FAQs on Geometric Shapes

What are different geometric shapes in Maths?

There are various geometric shapes such as circle, square, rectangle, kite, triangle etc. are the basic 2d shapes while Cube,Cuboid,Cone,Cylinder,Sphere are basic 3d shapes.

Name different kinds of polygons.

The different polygons are:
Triangle
Quadrilaterals – square, rectangle, parallelogram, trapezium, kite
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon

Give a few real-life examples of 3D shapes.

Cube – Sugar cube, Rubik’s cube
Cuboid- A wooden rectangular box, matchbox
Cone- Icecream cone, Pyramid
Sphere- Football, Basketball
Cylinder- Gas cylinder, Cylindrical jar

What are basic solid shapes?

The basic solid shapes are Cube, Cuboid, Cone, Sphere, Hemisphere and Cylinder.