Question

find the volume of the right prism whose altitude is 15cm & whose base is enclosed by an equilateral triangle with side 6m long.

Answer 1

The equilateral triangle can be considered to consist of two back-to-back right triangles. If the prism has a triangular base, then the base of the right prism could be one of these right triangles, so its area would be half the area (9√3cm²) of the equilateral triangle=4.5√3cm². The volume of the prism is 15×4.5√3=67.5√3=116.91cm³ approx.

If the equilateral triangle is the entire base of the prism, then the volume would be 233.82cm³ approx.

If the prism has a rectangular base then there are many rectangles that could fit into an equilateral triangle. The question doesn't say whether it's a triangular, square or rectangular prism. A rectangular prism is also called a cuboid.