- Introduction to 2D and 3D shapes
- Vertex
- Edge
- Face
- Let us know more about cubes
- Properties of cubes
- What are cuboids? How many faces, vertices, and edges do they have?
- How are 2D shapes used to create cubes?
- Let us know more about some 2D shapes
- What is a Rectangle?
- Properties of a Rectangle
- What is a Square?
- The difference between a Square and a Rectangle
- Solved Examples
- Frequently Asked Questions
2D shapes:
The abbreviation “2D” stands for two-dimensional shapes. They can be measured only by two measures. 2D shapes are completely flat and can be drawn only on paper, or for that matter a flat plane.
Examples: Triangle, Rectangle, Square, Circle
3D shapes:
On the other hand, the abbreviation “3D” stands for three-dimensional shapes. 3D shapes have three measures, like height, width, and breadth. There are other terms associated with two-dimensional shapes such as vertices and edges.
Examples: Notebook, Phone, Rubik’s Cube
Consider your classroom, which is a room and is a 3D structure. To construct a room, architects work on designs that portray a 3D image on a flat surface with the use of sophisticated software. They do so by first sketching the classroom, which has a cube-like structure. There are certain terms related to the drawing of a cube that make the task more convenient for architects. Let us look at some of these:
Vertex
The intersection of two or more line segments is known as the vertex. An intersection or a junction at which two roads meet is called a vertex, in case of a real world example of a vertex.
Example:
As we can see in the above figure, the vertex is the intersection of three lines in a cube. A cube has a total of 8 vertices.
Edge
A line segment joining the two vertices is called the edge. Having mentioned this fact, a cube has 12 edges.
Face
A solid object’s individual flat surface is known as its face.
In other words, the face is the planar region that forms the boundary of any solid figure.
Example: A square resembles a face. The top of the cube puzzle is a flat surface that is called the face. Every cube has a total of 6 faces, just like a cubic dice with 6 faces.
Let us learn more about cubes
Cubes are one of the basic three-dimensional solid shapes that have six faces. The six faces of a cube are all squares and are two-dimensional in shape.
In a cube, the three dimensions, which are the width, height, and length are all equal.
A cube also has 8 vertices and 12 edges, with three of the edges meeting at one vertex.
Properties of cubes
(i) All of the faces of a cube are squares.
(ii) All of the faces or sides are of the same size.
(iii) Each of the four faces comes into contact with the others at different vertices.
What are cuboids? How many faces, vertices, and edges do they have?
A cuboid is a three-dimensional figure with three pairs of rectangular faces attached in a box-like shape. A cuboid has six faces, each of which has equal dimensions as the side or face opposite to it. Furthermore, two of these six faces could be squares. Rectangular boxes, rectangular parallelepipeds, and right prisms are other names for cuboids.
Example: Book, Carton, lunch box
How are 2D shapes used to create cubes?
The structure of a cube comprises 6 squares. To create the 3D shape of a cube, we need 6 faces.
(i) First, put the two squares parallel to each other.
(ii) Now join the two faces on the side.
(iii) Join the bottom and the top in the above shape.
The result will be a cube that has 6 square faces.
Let us know more about some 2D shapes
What is a Rectangle?
A rectangle is a four-sided structure. The opposite sides of the rectangle are equal. Each corner, or vertex, has two sides meeting each other, just like a square. A rectangle differs from a square in that its opposite sides are of equal length.
Also, a rectangle is a two-dimensional flat shape.
Example: TV screen, piece of paper, and surface of a table.
Properties of a Rectangle:
(i) A rectangle has four vertices and four edges.
(ii) The length and breadth are not equal.
(iii) The opposite sides of the rectangle are equal.
What is a Square?
A square is a two-dimensional or 2D shape with four equal sides and four vertices.
The difference between a Square and a Rectangle
All four sides of a square are equal. But when we speak of a rectangle, only the opposite sides are equal in length.
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Solved Examples
Example 1 : How many square tiles cover this rectangle?
Answer: Number of rows = 2
Number of columns = 5
Adding the rows : 5+5=10
Adding the columns : 2+2+2+2+2=10
Hence, there are 10 square tiles in the rectangle
Example 2 : You use foam mats to cover the entire floor of a square room. You fit 2 mats across one side of the room. How many rows and columns of mats will you have?
Answer: The required number of foam mats to cover the entire floor of a square =2
One square foam mat contains = 1 row and two columns.
So, two square foam mats will contain 2 rows and 2 columns.
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A cube is a three-dimensional shape whereas a square is a two dimensional shape.
A cube is also made up of 6 square faces.
A cube is a square prism, and a cuboid on the other hand, is a rectangular prism. All sides of the cube are equal, and when we speak of a cuboid, the faces of the cuboid are not equal. All the faces of a cube are squares, but the faces of a cuboid are rectangles.