# Pentagonal Pyramid

Sub Topics
Pyramid is a structure of a polygon with the upper part converging to a fixed point. The converging fixed point is called apex.

There are mainly two parts for a pyramid. They are apex and base. Apex is the converging fixed point and the bottom part of the pyramid is called base of the pyramid.

Pyramids are usually named according to their bases. The important types of pyramids are

1)    Triangular Pyramid
2)    Square pyramid
3)    Pentagonal Pyramid
4)    Hexagonal Pyramid

Pyramids are again divided into oblique and regular based on the shape of the base.

Lets consider Pentagonal pyramid.

Pentagonal Pyramid

A pyramid with a Pentagonal base is called Pentagonal pyramid.

The figure of a triangular pyramid is shown below

### Pentagonal Pyramid Faces

A pentagonal pyramid has 6 faces. Top you can see 5 sides faces which are triangular in shape and base which is a pentagon.

## What is a Pentagonal Pyramid?

A Pentagonal pyramid has 6 faces. It has 5 sides faces, which are triangular in shape and a bottom, base which is a Pentagon. Since the bottom face is Pentagon in shape, the name of the solid is Pentagonal pyramid. There are 6 vertices and 10 edges to a Pentagonal pyramid.

## Pentagonal Pyramid Net

A net is a pattern that we can cut and fold to make a model of the solid. The net of Pentagonal pyramid consists of 5 triangles and a Pentagon. The base of the pyramid is a Pentagonal and the five lateral faces are triangles.

The net of the Pentagonal pyramid is given below.

We can fold the outer five triangles to form the Pentagonal pyramid.

## Volume of a Pentagonal Pyramid

Volume is the total area in the inner part.  We can say that it is the amount of water the solid will replace when immersed in a container of water.

### Volume of a Pentagonal Pyramid Formula

V = ($\farc{1}{3}$) x Base area x h

where and h is the height of the Pentagonal pyramid.
How do you Find the Volume of a Pentagonal Pyramid

## Surface Area of a Pentagonal Pyramid

Surface area is the total area on the outer part of the pyramid.  Surface area is divided into two. 1) Lateral surface area  2) Base area

Lateral surface area is the area of the lateral faces of the pyramid.  That is, in the case of the pentagonal pyramid, the area of the five lateral faces constitutes the lateral surface area.

Base area is the area of the base of the pyramid.

### Surface Area of a Pentagonal Pyramid Formula

Surface area = Base area + Lateral surface area

S = Base area + $\frac{1}{2}$ x perimeter of the base x slant height.
How do you Find the Surface Area of a Pentagonal pyramid