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

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 + b^{2}

Here, let us use the formula

2 x 4 x 5 + 4^{2} = 40 + 16 = 56 cm^{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 + b^{2}

Here, let us use the formula

= 2 x 24 x 15 + (24)^{2}

= 720 + 576

= 1296 cm^{2}