20. Which of the following three-dimensional figures has five vertices and five faces?
Answer: A
A rectangular pyramid has five vertices and five faces.
A rectangular pyramid is a three-dimensional figure that consists of a rectangular base and four triangular faces that meet at a single vertex (the apex). This configuration results in a total of five vertices and five faces.
A) A rectangular pyramid
This option is correct because a rectangular pyramid features one rectangular base and four triangular faces, totaling five faces. Additionally, it has five vertices: four at the base corners and one at the apex.
B) A triangular pyramid
A triangular pyramid, also known as a tetrahedron, has four triangular faces and four vertices. Therefore, it does not meet the criteria of having five vertices and five faces, making this option incorrect.
C) A rectangular prism
A rectangular prism has six faces (all rectangular), eight vertices, and twelve edges. Consequently, it does not satisfy the requirement of having five vertices and five faces, rendering this option incorrect.
D) A triangular prism
A triangular prism consists of two triangular bases and three rectangular faces, resulting in a total of five faces and six vertices. While it has five faces, it fails to meet the vertex requirement, thus making this option incorrect.
Conclusion
The rectangular pyramid is definitively the correct answer due to its unique structure of five vertices and five faces. All other options either fall short of the required number of vertices or faces, confirming that they do not fit the criteria established by the question.