Pyramid Whole Surface Area

The pyramid base can be of different shapes such as pentagon, square and triangle. An isosceles triangle is the shape of faces. Apex is defined as the part of a triangle and is the meeting point of every triangle of the pyramid. The diagonal height is known as the slant height and is in the centre of the base edge. It has been denoted as 1 to the apex.  Pyramid whole surface area can be defined as the total area of the lateral faces. The height of the pyramid is denoted as h and is the perpendicular distance to the base from the apex.

What is the surface area of the Pyramid? 

The surface area of any object can be stated as the area that is being occupied by the object’s surface. The square unit is the measuring unit of surface area. The whole surface area of the pyramid will contain the sum of every face of the lateral side. A Pyramid can be a regular triangular pyramid or square pyramid. The whole surface area of the pyramid can be solved by combining the area of the base and all of the faces. Therefore it can be said that by adding base area to 3 times of face area, the surface area can be formulated. The surface area of a square pyramid can be defined as the sum of its base and the sum of lateral faces. A square pyramid consists of four sides face of a triangle and a square base. Triangles are congruent and isosceles coincide with the square base. A pentagonal pyramid consists of a pentagon base and five triangles which will be the lateral bases. It consists of 6 vertices and 10 edges. A hexagonal pyramid consists of a hexagonal base and six triangle faces. It has 12 edges, 7 faces and 7 vertices. These triangular faces will meet at a point and the point is termed as a vertex. 

Pyramid whole surface area formula

The surface area of the pyramid is dependent on its base. The base of the pyramid can be square or can be regular. In the case of a regular pyramid, the following formula is used to calculate its surface area :

Surface area = base area + each lateral faces area

The regular pyramid surface area can be calculated as:

Base area + ½ p*s

Here, p is denoted as the perimeter of the base and s is used to denote slant height.

The square pyramid surface area can be calculated as:

b2 + 2bs

Here, b is denoted as base length and s is used to denote slant height. 

In the case of a triangular pyramid, the area of the triangle can be calculated as A = ½ bh, where b is denoted as triangle base and h is denoted as the height of the triangle.

Therefore formula of surface area becomes SA = A + 3(½ bh)

It can be further simplified as SA = A + 3/2bh

Here h signified the height of anyone’s pyramid face. B signifies the base of anyone’s pyramid face and also the length of anyone’s pyramid base side. 

For example, if the height of the face is 20 units, the base is 12 units and the pyramid base area is 32 units then the pyramid surface area is SA = 32 + (3/2)(12)(20) = 392 square units. 

When a non-regular pyramid is considered, each face area is calculated and an individual pyramid base. It is finally added. 

The formula can be stated as SA = area of base + area of first face + area of second face + area of the third face. 

Pentagonal pyramid surface area can be calculated through the following formula:

 SA = 5/2 * b(a+s)

Here, a is denoted as pentagonal pyramids apothem length, b is denoted as pentagonal pyramid base length and s is denoted as pyramid’s slant height.

Hexagonal pyramid surface area can be calculated as:

SA = 3ab + 3bs

Here a is denoted as pyramid apothem, b is denoted as base and s are denoted as pyramid’s slant height.

Application of pyramid 

Several applications of pyramids have been noticed. The more important usage of pyramids is the transmission of line towers. Electricity is needed to transfer from their generating station to their further substations. HT transmission lines have been used for transferring high voltage current. High voltage cables are connected with high electric towers. The towers are triangular lateral surfaces meeting at a vertex and have a polygon base. The most common example of a pyramid is the usage of prisms. Prism is a triangular pyramid that is used to study the concept of reflection and refraction.  Seral other applications of the pyramid are paperweights, making of home decor, tents and toys of kids. 

Conclusion

It can be concluded that several types of pyramids are there. It consisted of a triangular, square, right or oblique pyramid. Pyramids can also be divided into regular and irregular pyramids. The whole surface area of the pyramid consists of lateral sides and base areas. It can be termed as a polyhedron that is being formed by joining vertices. It has been generally classified based on the base of the polygon. It is being noticed that a pyramid with n number of bases consists of n+1 number of vertices. Each pyramid has its formula for calculating surface area and has been entitled to earlier