[b]A [u]prism[/u] is a solid object with:[/b][br][list][*]identical ends[/*][*]flat faces[/*][*]and the same [b][url=https://www.mathsisfun.com/geometry/cross-sections.html]cross section[/url][/b] all along its length![/*][/list][br]A [b]cross section[/b] is the shape made by cutting straight across an object.[br][img width=173,height=186]https://www.mathsisfun.com/geometry/images/prism-cross-section.jpg[/img][br]The cross section of this object is a [b]triangle[/b] ...[br].. it has the same cross section all along its length ...[br]... so it's a [b]triangular prism.[br][br][br][b][b][u]Bases[/u]: [/b]The ends of a prism are parallel [br]and each one is called a base.[/b][br][br] [img]https://www.mathsisfun.com/geometry/images/bases.svg[/img] [br][br][b][b][u]Sides:[/u] [/b]The side faces of a prism are [url=https://www.mathsisfun.com/geometry/parallelogram.html]parallelograms[/url] [br](4-sided shapes with opposite sides parallel)[br][/b][br] [img]https://www.mathsisfun.com/geometry/images/prism-sides-small.svg[/img] [br][/b][size=100][size=150][b][u][size=200]These are all Prisms:[/size][/u][br][br][/b][/size][/size][b]Rectangular Prism:    [/b] [b]Cross-Section:[br][/b][size=100][size=150][b][br][img]https://www.mathsisfun.com/geometry/images/cuboid.svg[/img] [img]https://www.mathsisfun.com/geometry/images/square.svg[/img][br][br]Cube:        Cross-Section:[br][br][img]https://www.mathsisfun.com/geometry/images/cube.svg[/img] [img]https://www.mathsisfun.com/geometry/images/square.svg[/img][br][br]Triangular Prism:     Cross-Section:[br][br][img]https://www.mathsisfun.com/geometry/images/tri-prism.svg[/img] [img]https://www.mathsisfun.com/geometry/images/triangle.svg[/img][br][br]Pentagonal Prism:     Cross-Section:[br][br][img width=175,height=106]https://www.mathsisfun.com/geometry/images/pentagonal-prism.png[/img] [img]https://www.mathsisfun.com/geometry/images/pentagon.svg[/img][br][br][br][size=200][u]Regular and Irregular Prisms:[/u][br][/size][br]All the previous examples are [b]Regular[/b] Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths, and equal angles.)[br]Here is an example of an [b]Irregular Prism[/b]:[br][table][tr][td]Irregular Pentagonal Prism:[/td][td] [/td][td] [b][table][tr][td]Cross-Section:[/td][/tr][/table][br][/b][/td][/tr][tr][td][br][img width=181,height=119]https://www.mathsisfun.com/geometry/images/irr-pentagonal-prism.png[/img][/td][td] [/td][td][img width=141,height=110]https://www.mathsisfun.com/geometry/images/irregular-pentagon.png[/img][/td][/tr][tr][td][br][/td][td][/td][/tr][tr][td]It is "irregular" because the [br]cross-section is not "regular" in shape.[/td][/tr][/table][br][/b][/size][/size][br][b][u][size=150][size=200]Surface Area of a Prism:[br][/size][br][/size][/u][/b][br] [img]https://www.mathsisfun.com/geometry/images/prism-area-perimeter.svg[/img][br] [br][b]Surface Area =  2 × Base Area + Base Perimeter × Length[br][/b][br][b][u]Example:[/u][/b] What is the surface area of a prism where the base area is 25 m[sup]2[/sup], the base perimeter is 24 m, and the length is 12 m: [br][br]Surface Area= 2 × Base Area + Base Perimeter × Length[br]  = 2 × 25 m[sup]2[/sup] + 24 m × 12 m[br]  = 50 m[sup]2[/sup] + 288 m[sup]2[/sup][br]  = [b]338 m[sup]2[/sup][/b][b][sup][br][/sup][/b][br]Use the area calculation tool to find the area of bases: https://www.mathsisfun.com/area-calculation-tool.html[br][br][size=200][b][u]Volume of a Prism:[/u][/b][br][/size][br]The Volume of a prism is the area of one end times the length of the prism.[br][br] [img]https://www.mathsisfun.com/geometry/images/prism-area-perimeter.svg[/img][br][b]Volume = Base Area × Length[/b][br][br][b][u]Example:[/u][/b] What is the volume of a prism where the base area is 25 m[sup]2[/sup] and which is 12 m long:[br][br]Volume= Area × Length[br]  = 25 m[sup]2[/sup] × 12 m[br]  = [b]300 m[sup]3[/sup][/b]