Difference Between Vertices and Edges

How Many Edges Does a Square Have?

Most people think that vertices and edges are the same things but in reality, they are not. Furthermore, vertices and edges are two different things and in this topic, you will learn about vertices, edges, the difference between vertices and edges using the example of Square. Because it is the most common shape and we can easily see how many edges does a square have.

Also, one of the most puzzling things about mathematics is the difference between vertices, faces, and edges. Furthermore, all these are parts of the geometrical shapes, but each is different from the other and is a separate shape. Besides, there are some tips that will tell you the difference between them.

Square

In geometry, the square is the most common and regular quadrilateral that means it has four equal sides and four equal angles. Moreover, all the angles of the square are \(90^{\circ}\). Also, the opposite sides of the square are parallel to each other and each side is perpendicular to the other.

Besides, the diagonal of the square bisect each other at \(90^{\circ}\). In addition, the diagonal bisect the vertices angle into two equal halves. Also, it will tell you how many edges does a square have?

What is a Vertex?

Simply it is a point where two lines meet. In simple words, the vertex is any sort of the corner. Furthermore, every corner of every geometrical shape signifies a vertex. Furthermore, the angle is irrelevant to whether or not a corner is a vertex. Also, the diverse shape has a different number of vertices.

For example, a square has four corners where a pair of lines meet so it has four vertices, in the same way, a triangle has 3 corners so it has 3 vertices. Similarly, a pentagon has five vertices, a hexagon has 6 vertices, and so on.

Besides, if we talk about 3D shapes then a square pyramid has five vertices (four in the bottom and one at the top), a cube has 8 vertices (four in the top and four in the bottom).

How Many Edges Does a Square Have?

Edges refer to the lines that join together to form the vertices. Also, it is a shape made up of its edges. Moreover, any two vertices joined by a line create an edge. Besides, it can be confusing because in 2D shapes there will only be as many edges as there are vertices.

For example, a triangle has 3 edges and 3 vertices. Also, a square has 4 edges and 4 vertices. But it can be easily understood with the help of 3-D shapes. For example, a square pyramid has 5 vertices and 8 edges that join it together. Similarly, a cube has 12 edges and 8 vertices.

What are the Faces?

There is one other element of geometrical shape which is the face. Also, the face of any shape separated it from the surrounding space by a closed outline of the edges. For example, in a cube four edges and four vertices combine to make a square face.

Besides, the 3-D shapes are usually made up of multiple faces, with the exception of a sphere that has one continuous face. Also, a square pyramid has 5 faces (4 triangle faces and 1 square base), and in a cube, there are six faces our side-by-side faces and one upper and one lower face.

Euler’s Formula

Euler formula is something that helps you to easily count the number of corners or lines without doing it manually. Besides, the number of vertices plus the number of faces minus the number of edges is always equal to 2. For example, let’s take the example of a square pyramid

Number of faces = 5
Vertices = 5
Edges = x
So, number of vertices + number of faces – number of edges = 2
5 + 5 – x = 2
x = 10 -2 = 8
So, the square pyramid has 8 edges.

Solved Question for You

Question. How many vertices and edges does a cuboid have?

A. 8 and 8

B. 8 and 12

C. 6 and 12

D. 12 and 8

Answer. The correct answer is option B because a cuboid has 8 vertices and 12 edges.

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