# Easy Methods to Find the Surface Area of a Pyramid

A pyramid is quite an intriguing geometrical object, with many interesting properties. In this post, we present the surface area formula for it.

Omkar Phatak

Last Updated: Jan 12, 2019

Some Interesting Facts

A pyramid is a '

*polyhedron*', which literally means 'many headed' object. A polyhedron is any three-dimensional object, that is characterized by completely flat faces and straight edges.*a geometry term for multi-sided, closed two-dimensional object*), connected with a point, which is known as the apex. Every side of the polygonal base, connected with the apex point, forms a triangular surface.

*n*' sides, then it has '

*n + 1*' faces, '

*n + 1*' vertices, and '2

*n*' edges. For example, a pyramid with a square base will have

*n*= 4 sides, 5 faces, 5 vertices, and 8 edges. Another interesting property is its self-dual nature.

Formulas

After that brief sojourn into the appreciation of geometrical beauty, let us look at the surface area formulas.

*Total Surface Area of a Pyramid = Base Surface Area + Lateral Surface Area*^{2}or m

^{2}. Here are the formulas for various types of pyramids.

Triangular Pyramid

The simplest type of pyramid is the regular tetrahedron, with a triangular base and three lateral faces. All its faces are equilateral triangles, which simplifies calculation.

*Surface Area of Triangular Pyramid = 4 x (Surface Area of Each Equilateral Triangle Face) = 4 x (√3 a*^{2}/ 4) = √3 a^{2}*Total Surface Area of a Regular Pyramid (Square Base) = Base Area (Square Area) + Area of 4 Triangular faces = b*

^{2}+ 2bhwhere 'b' is the base length and 'h' is the slant height of each triangular face. Knowing the value of 'b' and 'h', the calculation is quite straightforward.

Rectangular Pyramid

There is another variety of pyramids, which has a rectangular base. Following is the formula:

*Surface Area of a Rectangular Pyramid = lb + bh + lh = lb + h (b+l) = Area of Rectangular Base + ½ x h x (Perimeter of Rectangular Base)**Surface Area of a Pyramid with Polygonal Base = Base Surface Area + [½ x (Base Perimeter) x Slant Height)]*