A pyramid is a polyhedron with a base and three or more triangular faces that meet above the base at a point (the apex). A square pyramid, sometimes known as a pentahedron, is a three-dimensional object with five faces. The Great Pyramid of Giza is a well-known example of such a pyramid in real life. 

Square pyramid:

A square pyramid is a three-dimensional geometric form with a square base and four triangular faces/sides that meet at a single point (called the vertex). Because of its five faces, it is termed a pentahedron. A square pyramid has the following features: 

1. An apex: The pyramid’s highest vertex or point  
2. Square shaped base 
3. Four triangular faces 

This pyramid is said to be an equilateral square pyramid if all of the triangular faces have equal edges.

The right square pyramid is formed when the peak of the pyramid is directly above the centre of its base, forming a perpendicular with the base. 

All pyramids are classified according to their foundations, such as: 

1. Rectangular pyramid
2. Triangular pyramid
3. Square pyramid
4. Pentagonal pyramid
5. Hexagonal pyramid 

Properties of square pyramid:

A square pyramid has the following characteristics:

1. It has five different faces. 
2. Triangles make up the four side faces. 
3. The foundation is square. 
4. Vertices are five (corner points). 
5. It has eight edges. 

Types of square pyramid:

The following are the several varieties of square pyramids: 

1. Equilateral square pyramid 
2. Right square pyramid 
3. Oblique square pyramid 

Equilateral square pyramid:

If all of the edges have the same length, the sides form equilateral triangles, and the pyramid is a square pyramid.

A single edge-length parameter, l, can be used to classify the Johnson square pyramid. The height h, surface area A, and volume V of a pyramid of this type are: 

• H = (1/√2)l¹
• A = (1+√3)l²
• V = (√2/6)l³ 

Right square pyramid:

All of the lateral edges of a right square pyramid are the same length, and the sides other than the base are congruent isosceles triangles.

The formula for surface area and volume of a right square pyramid with a base length of l and a height of h is: 

• Area = l² + l√(l)² + (2h)² 
• Volume = (⅓)xl²xh
• Lateral edge length = √h² + (l²/2) 
• Slant height = √h² + (l²/4) 

Oblique square pyramid:

An oblique square pyramid is one in which the peak of the square pyramid is not aligned with the centre of the square base. 

Square pyramid formula:

The volume, surface area, height, and base area of a square pyramid can all be calculated using formulas. Find the formulas for the following: 

1. Volume of square pyramid 
2. Surface area of square pyramid 
3. Lateral edge length 
4. Height of square pyramid 

Volume of square pyramid:

V = a²h/3 

Where, a = base edge length

              h = height 

Base area of square pyramid:

A square pyramid’s base is also a square. As a result, we may get the base area by calculating the square of the edge length. 

Base area = side x side = edge ²

Surface area of a square pyramid: 

A = a² + 2a√(a²/4) + h²

where a is the length of the base edge, and 

The height of a square pyramid is h. 

The entire surface area of a regular pyramid can be calculated using the following formula: 

T.S.A. = ½PI + B 

Where,

The perimeter of the base is denoted by P.

L the height of the slope and

B the base’s surface area. 

Lateral edge length:

e = √h² + (l²/2) 

where, h = height 

              I = base length 

Height of square pyramid:

e = √h² + (l²/4) 

Where, h = height

               I = base length 

Net of a square pyramid:

When the surface of a three-dimensional figure is put out horizontally, revealing each face of the figure, a net of a 3D shape is formed. Different nets can exist in a solid.

The square pyramid’s net will flatten the view, revealing all of the faces. When the net of the square pyramid is folded back, the original 3d shape is revealed.

The shape of a square pyramid is produced by one square and four triangles attached to the four corners of the square, as shown in the above net. As a result, the surface area of the square pyramid will be equal to the sum of its five faces. 

Conclusion: 

A square pyramid is a three-dimensional geometric object with a square base and four triangular sides connected at the vertex. It has five faces and is a polyhedron (pentahedron). A square pyramid has a square base and four triangles that are joined at the vertex. It has a square base and triangle side faces with a shared vertex.