Given:
Height of triangular base = 8 cm
Length of traingular base = 6cm
Height of pyramid = 12 cm
Let's determine the volume of Valeria's pyramid.
To find the volume of the triangular pyramid, apply the formula:
[tex]V=\frac{1}{3}(A\ast h)[/tex]
Where A is the area of the triangular base and h is the height of the pyramid
To find the area of the triangular base, apply the area of a triangle formula:
[tex]\begin{gathered} A=\frac{b\ast h}{2} \\ \\ A=\frac{6\ast8^{}}{2}=\frac{48}{2}=24cm^2 \end{gathered}[/tex]
To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}(A\ast h) \\ \\ V=\frac{1}{3}(24\ast12) \end{gathered}[/tex]
Solving further:
[tex]\begin{gathered} V=\frac{1}{3}(288) \\ \\ V=\frac{288}{3} \\ \\ \text{ V = 96 cm}^3 \end{gathered}[/tex]
Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.
ANSWER:
[tex]\text{ C. 96 cm}^3[/tex]
