Question

what three - dimensional figure has a total of 5 surfaces (the sum of the faces and base(s) together)? a(n) triangular rectangular triangular pentagonal hexagonal octagonal

Explanation:

Step1: Recall prism surface formula

A prism has 2 congruent bases (polygons) and lateral faces (rectangles). The number of surfaces (faces + bases) is \( 2 + \text{number of sides of base} \).

Step2: Analyze each option

• Triangular prism: Base is triangle (3 sides). Surfaces: \( 2 + 3 = 5 \).
• Rectangular prism: Base is rectangle (4 sides). Surfaces: \( 2 + 4 = 6 \).
• Pentagonal prism: Base is pentagon (5 sides). Surfaces: \( 2 + 5 = 7 \).
• Hexagonal prism: Base is hexagon (6 sides). Surfaces: \( 2 + 6 = 8 \).
• Octagonal prism: Base is octagon (8 sides). Surfaces: \( 2 + 8 = 10 \).

Step3: Determine the second dropdown

The first dropdown is "triangular", so the second should be "prism" (since a triangular prism has 5 surfaces: 2 triangular bases + 3 rectangular lateral faces).

Answer:

The first dropdown: A(n) triangular (selected). The second dropdown: prism (to complete "triangular prism", which has 5 surfaces).