So the volumeof this rectangularprismis cubicunits.Volumeof a RightPrism
Lookingat the volumeof right prismswith the sameheightand differentbasesyou can see a pattern.The
computedarea of eachbaseis givenbelow. The heightof all threesolidsis the same,.
Puttingthe data for eachsolid into a table,we get:
Solid Height Areaof base Volume
Box 10 300 3000
Trapezoid 10 140 1400
Triangle 10 170 1700The relationshipin eachcaseis clear. This relationshipcan be provedto establishthe followingformulafor
any right prism:
Volumeof a RightPrismThe volumeof a right prismis.where is the area of the baseof the three-dimensionalfigure,and is the prism’s height(alsocalled
altitude).
Example 12
Find the volumeof the prismwith a triangularequilateralbaseand the dimensionsshownin centimeters.To find the volume,first find the area of the base.It is givenby:The height(altitude)of the triangleis 10.38cm. Eachside of the trianglemeasures12 cm. So the triangle
has the followingarea.