Definition of Pentagonal Pyramid

A pentagonal pyramid is a 3D object with the base of a pentagon upon which five triangle-shaped faces meet at the apex. This apex forms at the top of the pentagonal pyramid and it combines the triangular faces and the pentagonal base together. In a regular pentagonal pyramid, the base is a regular pentagon with lateral faces shaped like equilateral triangles.

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:

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Definition of Pentagonal Pyramid

A pentagonal pyramid is a 3D object with the base of a pentagon upon which five triangle-shaped faces meet at the apex. This apex forms at the top of the pentagonal pyramid and it combines the triangular faces and the pentagonal base together. In a regular pentagonal pyramid, the base is a regular pentagon with lateral faces shaped like equilateral triangles....

Surface Area of a Pentagonal Pyramid

The surface area of a pentagonal pyramid has two types of surface areas, i.e., a lateral surface area and a total surface area, which are measured in terms of square units like m2, cm2, in2, ft2, etc....

Lateral Surface Area

The lateral surface area of a pentagonal pyramid is equal to the sum of the areas of its lateral faces, i.e., the five triangular faces. We know that the general formula to find the lateral surface area of a pyramid is:...

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:...

Formula of the Surface Area in terms of the Height of the Pyramid

We know that, Slant height of the pyramid (l) = √[(s/2)2 + h2] Now, Lateral Surface Area of the Pentagonal Pyramid (LSA) = 5⁄2 × s × √[(s2/4) + h2] Total Surface Area of the Pentagonal Pyramid (TSA) = 5⁄2 × s × [a + √(s2/4) + h2)]...

How to find the Surface Area of a Pentagonal Pyramid?

Let’s take an example to understand how to calculate the surface area of a pentagonal pyramid....

Solved Examples on Pentagonal Pyramid

Example 1: Calculate the lateral surface area of a pentagonal pyramid whose base length is 5 cm and slant height is 7 cm....

Pentagonal Pyramid – FAQs

What is a Pentagonal Pyramid?...

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