Question

which three - dimensional figure has nine edges?
rectangular prism
rectangular pyramid
triangular prism
triangular pyramid

Explanation:

To determine which three - dimensional figure has nine edges, we analyze the edge structure of each option:

1. Rectangular prism: A rectangular prism has 6 faces (all rectangles), 8 vertices, and \(12\) edges (4 for the top rectangle, 4 for the bottom rectangle, and 4 connecting the corresponding vertices of the top and bottom rectangles).
2. Rectangular pyramid: A rectangular pyramid has a rectangular base (4 edges) and 4 triangular faces, each with one edge connecting the base vertices to the apex. So in total, it has \(4 + 4=8\) edges.
3. Triangular prism: A triangular prism has two triangular bases. Each triangle has 3 edges, so the two bases contribute \(3\times2 = 6\) edges. Additionally, there are 3 edges connecting the corresponding vertices of the two triangular bases. So the total number of edges is \(6+3 = 9\) edges.
4. Triangular pyramid (tetrahedron): A triangular pyramid has a triangular base (3 edges) and 3 triangular faces, each with one edge connecting the base vertices to the apex. So in total, it has \(3 + 3=6\) edges.

Answer:

C. triangular prism