How many edges does a prism have? Please give an answer. Fast.
The Correct Answer and Explanation is:
A prism has 3n edges, where n is the number of sides of the polygonal base.
Explanation:
A prism is a three-dimensional shape with two identical polygonal bases connected by rectangular or parallelogram faces. The number of edges of a prism is determined by the number of edges of its base polygon.
- Base Polygon: The polygon at the base of the prism has n sides, meaning it has n edges.
- Top and Bottom Bases: Since the prism has two identical bases (top and bottom), each base contributes n edges, giving a total of 2n edges for both bases.
- Connecting Edges: There are also edges connecting the corresponding vertices of the top and bottom bases. For each vertex of the base, there is a vertical edge connecting it to the top or bottom, giving n vertical edges.
Thus, the total number of edges in a prism is:Total edges=2n+n=3n\text{Total edges} = 2n + n = 3nTotal edges=2n+n=3n
For example:
- A triangular prism has a base with 3 sides (n = 3), so it has 3 × 3 = 9 edges.
- A rectangular prism (which is a type of prism with a rectangular base) has a base with 4 sides (n = 4), so it has 3 × 4 = 12 edges.
The formula 3n works for any type of prism, regardless of the shape of the base polygon.
