3D dimensional geometry-We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height. The room you are sitting in can be described by these three dimensions. The monitor you're looking at has these three dimensions. Even you can be described by these three dimensions. In fact, the clothes you are wearing were made specifically for a person with your dimensions.

the world around us, there are many three-dimensional geometric shapes. In these lessons, you'll learn about some of them. You'll learn some of the terminology used to describe them, how to calculate their surface area and volume, as well as a lot about their mathematical properties. http://www.learner.org/interactives/geometry/

Polyhedron-A **polyhedron** is a solid with flat faces (from Greek poly- meaning "many" and -edron meaning "face").

Cube Dodecahedronhttp://www.mathsisfun.com/geometry/polyhedron.html

3D dimensional geometry-We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height. The room you are sitting in can be described by these three dimensions. The monitor you're looking at has these three dimensions. Even you can be described by these three dimensions. In fact, the clothes you are wearing were made specifically for a person with your dimensions.

In the world around us, there are many three-dimensional geometric shapes. In these lessons, you'll learn about some of them. You'll learn some of the terminology used to describe them, how to calculate their surface area and volume, as well as a lot about their mathematical properties. http://www.learner.org/interactives/geometry/__________________________________________________________________________________Polyhedron-A **polyhedron** is a solid with flat faces (from Greek poly- meaning "many" and -edron meaning "face").

Cube Dodecahedronhttp://www.mathsisfun.com/geometry/polyhedron.html__________________________________________________________________________________Non polyhedra-Polyhedra and Non-Polyhedra

There are two main types of solids, "Polyhedra", and "Non-Polyhedra":

Polyhedra :

*(they must have flat faces)* Cubes and

Cuboids (Volume

of a Cuboid) Platonic Solids Prisms Pyramids Non-Polyhedra:

*(if any surface is not flat)* Sphere Torus Cylinder Cone http://www.mathsisfun.com/geometry/solid-geometry... Prisms-A **cross section** is the shape you get when cutting straight across an object.

Square Prism: Cross-Section: Cube: Cross-Section: (yes, a cube is a prism, because it is a square

all along its length)

(Also see Rectangular Prisms ) Triangular Prism: Cross-Section: Pentagonal Prism: Cross-Section:

and more!

Regular and Irregular Prisms

All the previous examples are **Regular** Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths, and equal angles.)

Here is an example of an **Irregular Prism**:

Irregular Pentagonal Prism:

Cross-Section (It is "irregular" because the

Pentagon is not "regular" in shape) Volume of a Prism

The Volume of a prism is the area of one end times the length of the prism

Volume = Area × Length

Example: What is the volume of a prism whose ends have an area of 25 in2 and which is 12 in long:

Answer: Volume = 25 in2 × 12 in = 300 in3

(Note: we have an Area Calculation Tool)

Other Things to Know

The sides of a prism are parallelograms(flat shapes that have opposites sides parallel).

A prism can lean to one side, making it an**oblique prism**, but the two ends are still parallel, and the sides are still parallelograms!

But if the two ends are **not parallel** it is not** a prism**.

http://www.mathsisfun.com/geometry/prisms.html

______________________________________________________________________________ Pyramids-Pyramids

When we think of pyramids we think of the **Great Pyramids of Egypt**.

They are actually * Square Pyramids*, because their base is a Square.

Parts of a Pyramid

A pyramid is made by connecting a **base** to an **apex** Types of Pyramids

There are many types of Pyramids, and they are named after the shape of their base.

Pyramid Base Triangular

Pyramid:

Details >> Square

Pyramid:

Details >> Pentagonal

Pyramid:

Details >> Right vs Oblique Pyramid

... and so on ...

This tells you where the top (apex) of the pyramid is. If the apex is directly above the center of the base, then it is a Right Pyramid, otherwise it is an Oblique Pyramid.

Right Pyramid Oblique Pyramid Regular vs Irregular Pyramid

This tells us about the **shape of the base**. If the base is a regular polygon, then it is a Regular Pyramid, otherwise it is an Irregular Pyramid.

Regular Pyramid Irregular Pyramid

Base is Regular Base is Irregular Area and Volume

The Volume of a Pyramid

- 1/3 × [Base Area] × Height
The Surface Area of a Pyramid

When all side faces are the same:

- [Base Area] + 1/2 × Perimeter × [Slant Length]

When side faces are different:

- [Base Area]+[Lateral Area]

Notes On Surface AreaThe Surface Area has two parts: the area of the base (the

), and the area of the side faces (the**Base Area**).**Lateral Area**For

:**Base Area**It depends on the shape, there are different formulas for triangle, square, etc. See Areafor formulas, or our Area Calculation Tool

For

:**Lateral Area**When all the side faces are the same:

- Just multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is
*"base times height divided by*But if the side faces are different (such as an "irregular" pyramid) then add up the area of each triangular shape to find the total lateral area. - http://www.mathsisfun.com/geometry/pyramids.
- Clayton Bailey