Cross Section Of A Prism

Prism

A solid with two congruent parallel faces, where whatsoever cantankerous section parallel to those faces is congruent to them.

Try this Adjust the height of the prism beneath. Select examples of various types of prism.

A prism is a solid that has two faces that are parallel and congruent. These are called the bases of the prism. If you have any cantankerous section of a prism parallel to those bases by making a cutting through it parallel to the bases, the cross section will look only like the bases.

In the figure above, click 'bear witness cross-section' and elevate the cross section upward and downwardly. Note that it is always coinciding to the bases; that is, information technology always has the same shape and size. This is true for right and oblique prisms.

Naming

Prisms are named for the shape of the base. In the figure in a higher place, select the diverse examples of a prism in the pull-down menu. Note the way the name of the prism depends on the shape of the bases.

Regular and Irregular prisms

This as well follows the shape of the bases. If the bases are regular polygons, then the prism is also called a regular prism. Too, irregular prisms have bases that are irregular polygons.

Right vs oblique prisms

A correct prism is 1 where the bases are exactly 1 above the other every bit in the left epitome. This ways that lines joining corresponding points on each base are perpendicular to the bases.

In the figure above select "allow oblique" in the options bill of fare. The figure is a correct prism. If you drag the top orange dot sideways yous tin can make the prism oblique (or 'skewed'). Cantankerous sections parallel to the bases are still congruent to the bases.

For right prisms the side faces are rectangles
For oblique prisms they are parallelograms.

"Thick"polygons

Another way to call up about prisms is if they were polygons that have an added 3rd dimension of 'thickness'. In the figure in a higher place, press 'reset' and pull the top downwardly and then the length is zero. You now have a polygon. Every bit yous move information technology up y'all tin can run across that equally the height increases the polygon gets 'thicker'.

Volume of a prism

Is given past the area of a base of operations times the pinnacle. This is true for right and oblique prisms. Encounter Volume of a prism.

Surface area

The surface area of a prism is the sum of the areas of the bases and sides. For more, see Surface area of a prism.

Cylinders as prisms

Technically a cylinder is non a prism because its sides are curved. Just when the bases are regular polygons with a very large number of sides, they wait merely like cylinders and all the properties of cylinders apply to them. The volume adding is similar. This is explored further at Cylinder definition.

Prisms and rainbows

If you smooth a beam of white light through a triangular drinking glass prism, it will break the lite into its various wavelengths producing the characteristic 'rainbow'. In physics textbooks the prism is ordinarily drawn on its side as in the figure in a higher place.

In mathematics, a prism tin exist more than just that triangular shape, every bit is described in a higher place.

Things to try

In the applet at the top of the folio, select the different examples and realize that the bases of a prism can be literally any polygon.
For each example, check the "show cross department' box, and slide the department up and down, showing that the cross section is the same everywhere.
For each example, check 'Allow oblique' and elevate the top to the right, demonstrating the deviation between a right and oblique prism. Arrange the cross section to show information technology is abiding for oblique prisms too.
Click on 'hide details'. Perform all the higher up and guess the full correct name of the prism. Then click 'testify details' to check your answer.