# Year 10+ 3D Geometry

### Chapters

### Pentagonal Pyramid

# Pentagonal Pyramid

A `pentagonal pyramid`

is a polyhedron (flat-sided three-dimensional figure), which has a pentagon as its base, and five faces, shaped like triangles, that meet at a point, called the `apex`

.

Pentagonal pyramids have six faces, six vertices and ten edges.

## Building a Pentagonal Pyramid

You can make a pentagonal pyramid yourself by using a template like the following `net`

(template), cutting it out along the outside lines, folding it along the inside lines and taping it together along the edges.

## Finding the Surface Area and Volume of a Pentagonal Pyramid

### Finding the Surface Area of a Pentagonal Pyramid

We can split the surface area of a pentagonal pyramid up into two parts:

- The Area of the Base.
- The Area of the Slanted Sides

When the slanted sides are all the same, the surface area of the pentagonal pyramid is given by the formula:

### Finding the Volume of a Pentagonal Pyramid

Like any pyramid, the volume of the pentagonal pyramid is equal to \(\dfrac{1}{3}\) the volume of the pentagonal prism with the same height and base. So,

### Description

There are several lessons related to 3D geometry such as

- Euler's formula
- Vertices, Edges and Faces
- Volumes of 3D shapes
- etc

Even though we've titled this lesson series to be more inclined for Year 10 or higher students, however, these lessons can be read and utilized by lower grades students.

### Prerequisites

Understanding of 3D shapes

### Audience

Year 10 or higher, but suitable for Year 8+ students

### Learning Objectives

Get to know 3D Geometry

Author: Subject Coach

Added on: 27th Sep 2018

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