Surface Area of a Pyramid Formula

In geometry, a polyhedron made by joining a polygonal base with a point, known as the apex, is called a pyramid. Each lateral face’s base edge and apex form a lateral face in a triangle.

The sum of the area of all its faces is the surface area of the pyramid. There are n + 1 vertices, n + 1 faces, and 2n edges in a pyramid with an n-sided base. The apex of the pyramid is the top vertex.  A pyramid is said to be formed by connecting the bases to an apex. The perpendicular distance between the apex and the base is the height of the pyramid.

The types of pyramids are mentioned below

• Triangular pyramid – No. of Faces = (3+1) = 4

                                        No. of Vertices: (3+1) = 4

                                        No. of Edges: 2(3) = 6

• Square pyramid- No. of Faces: (4+1) = 5

                                 No. of Vertices: (4+1) = 5

                                 No. of Edges: 2(4) = 8

• Pentagonal pyramid- No. of Faces: (5+1) = 6

                                         No. of Vertices: (5+1) = 6

                                         No. of Edges: 2(5) = 10

Let us take some examples of the surface area of a pyramid formula

1. Find out the Surface area of the square pyramid with a side of 5 cm and a base of 4 cm?

Solution

Surface area of a square pyramid = 2bs + b²

Here, let us use the formula

 2 x 4 x 5 + 4² = 40 + 16 = 56 cm²

2. What is the surface area of the square pyramid that has a side of 15 cm and a base of 24 cm? 

Solution 

Surface area of a square pyramid = 2bs + b²

Here, let us use the formula

= 2 x 24 x 15 + (24)²

= 720 + 576

= 1296 cm²