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    Topics || Problems

    One part of a quartz crystal is a hexagonal prism with a right section of 1.29 sq. in., an edge of 2.31 in, and a base of 1.41 sq. in. Find the altitude of the prism.

    Volume of a prism can be calculated in two ways

    \(V = A_{base}~x ~altitude\)

    \(V = A_{right ~section}~x~lateral~edge\)

    Equate both equations and isolate \(altitude\)

    \( base~x ~altitude = right ~section~x~lateral~edge\)

    \(altitude = \frac{A_{right ~section}~x~lateral~edge}{A_{base}}\)

    \(altitude = \frac{1.29 (2.31)}{1.41}\)

    \(altitude = 2.11 ~ft\)