Answer: To find the volumes of the prism and pyramid with congruent triangular bases and heights of 15 m, we need to know the dimensions of the triangular bases.
Let's assume that the triangular bases are equilateral triangles with side length 's'. The formula to calculate the volume of a prism is given by:
Volume of Prism = Base Area * Height
The base area of an equilateral triangle can be found using the formula:
Base Area = (sqrt(3) / 4) * s^2
Substituting the values, the volume of the prism is:
Volume of Prism = (sqrt(3) / 4) * s^2 * 15
Now, let's calculate the volume of the pyramid. The volume of a pyramid is given by:
Volume of Pyramid = (1/3) * Base Area * Height
Substituting the base area and height values for the pyramid:
Volume of Pyramid = (1/3) * ((sqrt(3) / 4) * s^2) * 15
Simplifying the equations, we can calculate the volumes of the prism and pyramid.
Please provide the value of 's' (side length of the triangular base) to proceed with the calculations.