Math  /  Geometry

Questionhttps://www.carnegielearning.com/apps/k12/9.9.30/sap/\#/tutor/95?configUrl=https:\%2F\%2Fwww.carnegielearning.com\%2. MATHiaU Calculating Volume of Right Prisms Home Audio Support < Unit Overview Step-by-Step Solver Sample Problem Hints
Your friend bought a piece of jewelry with a gem stone. The gem stone is a right triangular prism.
In the prism, segment DF=2.9D F=2.9 centimeters, segment EG=2.5E G=2.5 centimeters, and segment AD=0.87A D=0.87 centimeters.
What is the volume of the gem stone? Use the given information to complete the worksheet. \begin{tabular}{|r|l|c|} \cline { 2 - 3 } & \multicolumn{1}{c|}{ Value } & Units \\ \hlineDF\overline{D F} (base of DEF)\triangle D E F) & & centimeters \\ \hlineEG\overline{E G} (height of DEF)\triangle D E F) & & centimeters \\ \hline Area of DEF\triangle D E F & & square centimeters \\ \hlineAD\overline{A D} (height of right prism) & centimeters \\ \hline Volume of the Gem Stone & & cubic centimeters \\ \hline \end{tabular}

Studdy Solution
Use the area of the triangular base to calculate the volume of the prism using the formula for the volume of a prism:
V=Base Area×Height of Prism V = \text{Base Area} \times \text{Height of Prism}
Substitute the known values:
V=3.625cm2×0.87cm V = 3.625 \, \text{cm}^2 \times 0.87 \, \text{cm}
Calculate the volume:
V=3.15675cm3 V = 3.15675 \, \text{cm}^3
The volume of the gem stone is:
3.15675cm3 \boxed{3.15675 \, \text{cm}^3}

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