Total Surface Area
The total surface area of a pentagonal pyramid is equal to the total area covered by its five triangular side faces and the pentagonal base. We know that the general formula to find the total surface area of a pyramid is:
Total Surface Area (TSA) = LSA of the pyramid + Area of the base
Area of the pentagonal base = 5⁄2 (a × s)
So, the total surface area = 5⁄2 (s × l) + 5⁄2 (a × s) = 5⁄2 × s × (l + a)
Total Surface Area = 5⁄2 × s × (a + l)
where,
“s” is the side length of the base,
“a” is apothem length of the base, and
“l” is the slant height of the pyramid.
Area of a Pentagonal Pyramid
In geometry, a pentagonal pyramid is a three-dimensional figure with a pentagonal base upon which five triangular faces are erected and meet at a meeting point called the apex. It has six faces, i.e., a pentagonal base and five triangular faces, six vertices, and ten edges. In a pentagonal pyramid, each edge of the pentagonal base is connected to the apex, and thus the five triangular/lateral faces are formed. A regular pentagonal pyramid is a pyramid that has a regular pentagonal base, and its lateral faces are equilateral triangles. Based on the shape of the polygonal base of a pyramid, every pyramid has a different formula. In this article, we will discuss the surface area of a pentagonal pyramid in detail.
Table of Content
- Definition of Pentagonal Pyramid
- Surface Area of a Pentagonal Pyramid
- Lateral Surface Area
- Total Surface Area
- Formula of the Surface Area in terms of the Height of the Pyramid
- How to find the Surface Area of a Pentagonal Pyramid?
- Solved Examples on Pentagonal Pyramid
- Related Resources: