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Which of the following is true about a t...

Which of the following is true about a triangular prism?

A

It has 2 triangular faces.

B

It has 3 rectangular faces.

C

It has 6 vertices.

D

All of these

Text Solution

AI Generated Solution

The correct Answer is:
To determine which statements about a triangular prism are true, we need to analyze the properties of a triangular prism step by step. ### Step-by-Step Solution: 1. **Identify the Faces of the Prism:** A triangular prism has two triangular bases and three rectangular lateral faces. - **Triangular Faces:** There are 2 triangular faces (the top and bottom). - **Rectangular Faces:** There are 3 rectangular faces (the sides connecting the triangular bases). **Conclusion:** The statement that it has two triangular faces is **true**. 2. **Count the Rectangular Faces:** As mentioned, the three lateral faces of the prism are rectangles. - The three rectangles connect the corresponding sides of the two triangular bases. **Conclusion:** The statement that it has three rectangular faces is **true**. 3. **Count the Vertices:** A vertex is a corner point where the edges meet. - For a triangular prism, there are 3 vertices on the top triangular face and 3 vertices on the bottom triangular face, making a total of 6 vertices. **Conclusion:** The statement that it has six vertices is **true**. 4. **Summarize the Findings:** Since all the statements provided in the options are true: - It has two triangular faces. - It has three rectangular faces. - It has six vertices. Therefore, the correct answer is that **all of these statements are true**. ### Final Answer: The correct option is **4. All of these**.

To determine which statements about a triangular prism are true, we need to analyze the properties of a triangular prism step by step. ### Step-by-Step Solution: 1. **Identify the Faces of the Prism:** A triangular prism has two triangular bases and three rectangular lateral faces. - **Triangular Faces:** There are 2 triangular faces (the top and bottom). - **Rectangular Faces:** There are 3 rectangular faces (the sides connecting the triangular bases). ...
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