Question

How many triangular surfaces are there in the given combination of solids?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

Be careful to read whether the question asks for the triangular faces of the upper solid alone (which would be 6) or the entire combination (which is 8).

Answer 1

The Correct Option is D

Step 1: Identifying the Component Solids from the Drawing:
The drawing on Page 14/15 depicts a combination of two solids:
• Upper Solid: An upright regular hexagonal pyramid.
• Lower Solid: A horizontal triangular prism resting on one of its rectangular faces.

Step 2: Counting the Triangular Faces on Each Solid:

• Hexagonal Pyramid (Upper Solid): A hexagonal pyramid has $6$ triangular lateral faces meeting at the apex.
• Triangular Prism (Lower Solid): A triangular prism is bounded by $3$ rectangular lateral faces and $2$ triangular bases/end faces.

Step 3: Total Count:
Summing the triangular faces of both components: $$\text{Total triangular surfaces} = 6 \text{ (from pyramid)} + 2 \text{ (from prism)} = 8$$ Therefore, option (D) is the correct answer.