How many vertices does a rectangular prism has? a. 4 b. 6 c. 8 d. 10
The correct answer and explanation is:
Correct Answer: c. 8
A rectangular prism is a three-dimensional geometric solid that has six faces, all of which are rectangles. It is also known as a cuboid. To understand how many vertices a rectangular prism has, it is important to examine its structure carefully.
Each corner point where the edges of the prism meet is called a vertex. In a rectangular prism, there are three dimensions—length, width, and height. The shape has two identical rectangular faces on the top and bottom, two on the front and back, and two on the sides.
When a rectangular prism is visualized or drawn, it is seen to have eight corner points. These are the points where three edges meet, and they are not all in the same plane. Each of the three pairs of opposite faces contributes to forming the corners or vertices. Specifically, the base has four vertices, and the top face, which is congruent to the base, has another four vertices. This results in a total of eight vertices.
The relationship between the number of faces, edges, and vertices of any polyhedron is described by Euler’s formula:
V – E + F = 2,
where V is vertices, E is edges, and F is faces.
For a rectangular prism:
- Faces (F) = 6
- Edges (E) = 12
- Vertices (V) = 8
Substituting into Euler’s formula:
8 – 12 + 6 = 2,
which confirms that the count is correct.
Understanding the structure of a rectangular prism is essential in geometry because it serves as the foundation for learning about volume, surface area, and spatial reasoning. Recognizing that it has 8 vertices helps in visualizing and solving problems involving three-dimensional shapes.