Question

what three - dimensional solid has 6 rectangular faces, 2 equal bases that are not rectangles, and 18 edges? triangular prism pentagonal prism hexagonal prism octagonal prism

Explanation:

1. Recall the properties of prisms: A prism has two congruent (equal) polygonal bases and rectangular lateral faces. The number of lateral faces equals the number of sides of the base polygon. The total number of faces is 2 (bases) + number of lateral faces. The number of edges: for a prism with an n - sided base, the number of edges is 3n (n edges for each base and n lateral edges connecting the corresponding vertices of the bases).
2. Analyze each option:

• Triangular prism: A triangular prism has a triangular base (3 - sided). Number of lateral faces = 3, total faces = 2+3 = 5 (not 6). Number of edges: 3×3 = 9 (not 18).
• Pentagonal prism: A pentagonal prism has a pentagonal base (5 - sided). Number of lateral faces = 5, total faces = 2 + 5=7 (not 6). Number of edges: 3×5 = 15 (not 18).
• Hexagonal prism: A hexagonal prism has a hexagonal base (6 - sided). Number of lateral faces = 6, total faces = 2+6 = 8? Wait, no. Wait, the problem says 6 rectangular faces. Wait, the two bases are not rectangles, so the lateral faces are rectangles. For a prism, the lateral faces are rectangles. The number of lateral faces is equal to the number of sides of the base polygon. The total number of faces is 2 (bases) + number of lateral faces. Wait, the problem says 6 rectangular faces (so lateral faces = 6), and 2 non - rectangular bases. So total faces=6 + 2=8? Wait, no, maybe I misread. Wait, the problem says "6 rectangular faces, 2 equal bases that are not rectangles". So lateral faces = 6, bases = 2. Now, number of edges: for a prism with n - sided base, number of edges is 3n. If lateral faces = 6, then n (number of sides of the base) = 6 (since lateral faces = n). Then number of edges = 3×6 = 18. Let's check the faces: lateral faces = 6 (rectangular), bases = 2 (non - rectangular, hexagonal bases). That matches.
• Octagonal prism: An octagonal prism has an octagonal base (8 - sided). Number of lateral faces = 8, total faces=2 + 8 = 10 (not 6). Number of edges: 3×8 = 24 (not 18).

Answer:

hexagonal prism