# 12-2 Pap Prisms And Pyramids Homework

## Prisms

*Go to Surface Area or Volume.*

A prism is a solid object with:

- identical ends
- flat faces
- and the same
**cross section**all along its length !

A **cross section** is the shape made by cutting straight across an object.

The cross section of this object is a **triangle** ...

.. it has the same cross section all along its length ...

... so it's a **triangular prism.**

Then imagine it extending up from the sheet of paper ... |

## No Curves!

A prism is a polyhedron, which means all faces are flat!

For example, **a cylinder is not a prism**, because it has curved sides.

## Bases

The ends of a prism are parallel

and each one is called a base.

## Sides

The side faces of a prism are parallelograms

(4-sided shapes with opposite sides parallel)

## These are all Prisms:

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 cross-section is not "regular" in shape. |

## Surface Area of a Prism

Surface Area = 2 × Base Area

+ Base Perimeter × Length

### Example: What is the surface area of a prism where the base area is 25 m^{2}, the base perimeter is 24 m, and the length is 12 m:

Surface Area = 2 × Base Area + Base Perimeter × Length

= 2 × 25 m^{2} + 24 m × 12 m

= 50 m^{2} + 288 m^{2}

= **338 m ^{2}**

(Note: we have an Area Calculation Tool)

## Volume of a Prism

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

Volume = Base Area × Length

### Example: What is the volume of a prism where the base area is 25 m^{2} and which is 12 m long:

Volume = Area × Length

= 25 m^{2} × 12 m

= **300 m ^{3}**

## More About The Side Faces

The side faces of a prism are parallelograms (4-sided shape with opposites sides parallel)

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

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

PolyhedronCuboids / Rectangular PrismsPlatonic SolidsCylinderConeSphereTorus

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