2D and 3D Figures

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Geometry is a study of shapes. It is broadly classified into two types: plane geometry called as 2d shapes and solid geometry called as 3d shapes. Let us draw a picture of a notebook on a piece of paper. What we observe is a plain picture drawn on a paper. It does not occupy any space called as 2d shapes, but if we keep a real notebook on that piece of paper it occupies some space, and such shapes are called 3d shapes or three-dimensional shapes. 

Plane geometry or two-dimensional geometry deal with the flat figures that can be drawn on a piece of paper like line, curves, polygons, quadrilaterals, etc, while solid geometry or three-dimensional geometry deals with solid shapes or three-dimensional shapes. Examples of three-dimensional shapes are sphere, cylinders, cones, etc. 

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What are 2D Shapes?

In geometry, a shape or a figure that has two dimensions namely a length and a breadth is called a 2D shape. In other words, a plane object that has only length and breadth is a 2 dimensional shape. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides.

There are no fixed properties of the 2D shape. As each shape has a different number of sides and for each shape, properties vary. But, every 2D shape is flat and is enclosed.

A two-dimensional closed figure bounded with three or more than three straight lines is called a polygon. Triangles, square, rectangle, pentagon, hexagon, are some examples of polygons.

 For example, triangles and squares are polygons.


Examples of 2d Shapes:

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What are 3D Shapes?

The shapes that occupy space are called 3D shapes. 3D shapes can also be defined as the solid shapes having three dimensions length, width, and height. A football is an example of the sphere which is a three-dimensional figure while a circle drawn on a piece of paper is a two- dimensional figure. Similarly, we have many 3D shapes all around us like a table, chair, notebook, pen, etc. Here are some of the examples of three-dimensional shapes and properties of 3d shapes.

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Some of the Attributes of 3D Shapes are:

  • Faces: The 2d figures of the 3d shapes are called the faces of the 3D figures.

  • Edges: A line segment formed by the  two faces are called the edges of the 3D shapes.

  • Vertices: A corner point where the edges of the 3d shapes meet are called vertices.

Let us consider a 3d shape , a cube.The below figure represents faces, edges, and vertices of a cube.

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Here is the difference between 2d  and 3d shapes which will make the concept more clear.


Difference Between 2D and 3D Shapes

Basis for Comparison 

2D Shapes 

3D Shapes 

Basic

Only 2 dimensions are there that are length and width.

Three dimensions are there, length, width and height.

Shapes

Square, circle, triangle, rectangle, hexagon, etc.

Cube, sphere, cone, cuboid, etc.

Involves

Length and breadth

Length, breadth and height

Ease of construction

Simple to create

Quite complex

Edges

Are completely visible in the drawings.For example, in a square, all the edges are visible. 

Not visible or hidden due to overlapping.However, if we take an example of the cube, then, it is not possible to display all of its edges from one angle


Solved Examples:

Example 1:

Find the volume and surface area of a cuboid of l= 10cm, b = 8cm and h = 6 cm.

Solution: We have Volume of cuboid = V = l x b x h 

  =10 x 8 x 6

                                                        = 480cm2

             Surface area = 2 ( lb + lh + bh)

= 2( 10x8 + 10x6 + 8x6)

=2(80 + 60 + 48)

=376cm2


Example 2:

The length of the rectangular field is 15m and width is 6m. Find the area and perimeter of the field 

Solution:

Given that   Length = 15m

Width = 6m

We have,  Area formula A = length x width 

        = 15 x 6 

        = 90 m2

 And Perimeter formula P = 2 (length + width) 

         = 2 x (15 + 6) 

         = 2 x 21

        = 42 m.


Quiz Time

Find the area of the right-angled triangle whose base is 12cm and hypotenuse 13cm.

  1. 40 cm

  2. 85 cm

  3. 60 cm

  4.  30cm2


The side of a square whose surface area is 600cm is

  1. 10cm

  2. 20 cm

  3. 30 cm

  4. 40 cm


Fun Facts

  • 3D graphics are used in computers to make video games or animated movies. 

  • Some people consider time as a fourth dimension.

FAQ (Frequently Asked Questions)

1. Explain the Difference Between Area and Volume

Some of the key difference between area and volume in math are:


Area vs Volume

Area

Volume

The area is the measurement of the region covered by any two-dimensional geometric shapes.

The volume is the space occupied by the three-dimensional object.

The area is measured for plain figures

Volume is measured for 3D(solid) figures.

The area is measured in two dimensions i.e length and breadth.

Volume is measured in three dimensions i.e length, breadth, and height.

The area is measured in square units 

Volume is measured in cubic units.

The area covers the outer space of an object 

Volume is the capacity of an object

Example: square, rectangle, circle, etc.

Example: cube, cuboid, sphere, etc.

2. Explain the Difference Between Area and Surface Area

Area vs Surface Area

Area

Surface Area

The area is the measurement of the space occupied by any two-dimensional geometric shapes.

The surface area is the sum of areas of all the faces of the three-dimensional figure.

Plane 2D figures represent the area. Example: circles, rectangles, and triangles.

Solid 3D figures represent the surface area. Examples: cylinder, prisms, pyramids, and cones.

When we have to calculate area all we have to do is concentrate on the area of one figure.

In the surface area, when we have to calculate surface area, we have to work out on the area of all the faces.

Example: The formula of area for the rectangle is – length x width.

Example: The formula to calculate the surface area for a cuboid is – SA = 2lw+2lh+2hw.