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QuestionMathematics
How many faces, edges, and vertices does a triangular prism have?
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Answer
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Step 1:
First, let's clarify the properties of a triangular prism: - It has two congruent triangular bases (identical in shape and size). - It has three rectangular sides connecting the corresponding sides of the triangular bases.
Step 2:
- Therefore, a triangular prism has a total of 2 + 3 = $$\boxed{5}$$ faces.
Now, let's count the faces: - There are two triangular faces from the bases. - There are three rectangular faces from the sides.
Step 3:
- Since there are two triangular bases and three rectangular faces, we have 2 × 3 + 3 × 4 = $$\boxed{12}$$ edges.
Next, let's count the edges: - Each triangular base has three edges. - Each rectangular face has four edges.
Step 4:
- Since there are two triangular bases, we have 2 × 3 = $$\boxed{6}$$ vertices.
Finally, let's count the vertices: - Each triangular base has three vertices. - The rectangular faces share vertices with the triangular bases.
Final Answer
- A triangular prism has 5 faces, 12 edges, and 6 vertices.
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