# What Are Prisms & Pyramids?

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In math, a prism is a polyhedron made up of parallel top and bottom bases and rectangular side faces. Pyramids have one base and triangular side faces, which meet at a central vertex point. A dice or cube is an example of a prism. A traditional tent with flat faces that meet at one vertex and one base is an example of a triangular pyramid.

## Prisms

There are a variety of prism shapes, including square prisms, cube or rectangular prisms, triangular prisms and pentagonal prisms. Regular prisms are prisms whose cross section has equal lengths and angles. A cross section is the shape that remains when you cut straight across an object. Pentagonal prisms have irregular cross sections, because the angles and side lengths vary. Prisms have no curved sides.

Multiply the area of the prism’s parallel bases by its length to calculate its total volume.

## Drawing a Prism

Expand any two-dimensional shape to create a three-dimensional prism. To create a triangular prism, draw an equilateral triangle base on a piece of paper. Duplicate the triangle a few inches diagonally from the original shape. Use a ruler to join the points of one triangle to the corresponding points of the other triangle. Highlight the base by shading or coloring with marker.

To make a square prism, draw two equilateral squares diagonally from each other. Connect their corresponding points with straight lines.

## Pyramids

A pyramid is formed by connecting a base to the highest point of the shape, called an apex. There are several types of pyramids, which take the name of their base shape. For example, a triangle base forms a triangle pyramid, a square base forms a square pyramid and a pentagonal base forms a pentagonal pyramid.

A pyramid is called a right pyramid if the apex forms directly above the center of the base. If the apex appears elsewhere, it is considered an oblique pyramid. Regular pyramids have regular bases, where all of the sides are equal in length. Irregular pyramids have bases made up of unequal side lengths.

To find the volume of a pyramid, multiply height by the base area by 1/3.

## Drawing a Pyramid

To create a simple right pyramid, draw a slanted parallelogram on a piece of paper. This will be used as the base of your pyramid. Draw a small dot above the center of the base as the apex of your pyramid. Use a ruler to draw straight diagonal lines from each corner of the base shape to meet at the apex of the pyramid. Emphasize the base by coloring or shading it with a marker.