The volume formula for a triangular prism is:
In the figure, we already have the height of the prism and it is 10cm.
So, we need to figure out first the area of the triangle. The area of a triangle can be solved using the formula below:
where b = the length of the base of the triangle and h = height of the triangle.
In the triangle, the base is 6cm while the height is 4cm. Let's plug this in to the formula.
![\begin{gathered} A=(1)/(2)(6\operatorname{cm})(4\operatorname{cm}) \\ A=(1)/(2)(24cm^2) \\ A=12\operatorname{cm}^2 \end{gathered}]()
The area of the triangle is 12 cm². Going back to the formula of the volume of the triangular prism, we can now plug in the area of the triangle and the height of the prism that is 10 cm.
![\begin{gathered} V=12\operatorname{cm}*10\operatorname{cm} \\ V=120\operatorname{cm}^3 \end{gathered}]()
Therefore, the volume of the triangular prism is 120 cubic centimeters.