Which two solids have the same number of faces? A. A triangular prism and a rectangular prism B. A triangular pyramid and a rectangular prism C. A triangular prism and a square pyramid D. A triangular pyramid and a square pyramid
The Correct Answer and Explanation is:
The correct answer is C. A triangular prism and a square pyramid.
Here’s the reasoning:
- Triangular prism: A triangular prism consists of two triangular bases and three rectangular faces connecting the corresponding sides of the triangles. Therefore, the triangular prism has 5 faces in total: 2 triangular faces and 3 rectangular faces.
- Square pyramid: A square pyramid has a square base and four triangular faces that meet at a single apex. Therefore, the square pyramid also has 5 faces in total: 1 square face and 4 triangular faces.
So, both the triangular prism and the square pyramid have 5 faces, making option C the correct answer.
Now let’s review the other options:
- A. A triangular prism and a rectangular prism: A triangular prism has 5 faces, as mentioned. A rectangular prism, on the other hand, has 6 faces (4 rectangular faces and 2 square faces). Therefore, these solids do not have the same number of faces.
- B. A triangular pyramid and a rectangular prism: A triangular pyramid has 4 faces (3 triangular faces and 1 triangular base). A rectangular prism has 6 faces. Therefore, they do not have the same number of faces.
- D. A triangular pyramid and a square pyramid: A triangular pyramid has 4 faces (3 triangular faces and 1 triangular base), while a square pyramid has 5 faces (1 square face and 4 triangular faces). Therefore, these solids do not have the same number of faces either.
Thus, the only solids in the options with the same number of faces are the triangular prism and the square pyramid.
