A prism and pyramid have congruent triangle bases of the height are both 15 what is the volume
The volume of a prism or pyramid is calculated by multiplying the area of the base by the height and then dividing by 3 for a pyramid. Since both the prism and pyramid have congruent triangle bases with a height of 15, we can simply calculate the volume using the formula for a triangular prism or pyramid.
For a prism:
Volume = base area x height
Volume = (1/2 x base x height) x height
Volume = (1/2 x base x 15) x 15
Volume = 7.5 x base x 15
For a pyramid:
Volume = (1/3) x base area x height
Volume = (1/3 x (1/2 x base x height) x height
Volume = (1/3 x (1/2 x base x 15) x 15
Volume = (1/6 x base x 15) x 15
Volume = 2.5 x base x 15
Therefore, the volume of the prism or pyramid with congruent triangle bases of height 15 is represented by the formula 7.5 x base x 15 for a prism and 2.5 x base x 15 for a pyramid.