Question
Identify the polyhedron. Choose the correct answer below. A. Quadratic prism B. Pentagonal prism C. Quadratic pyramid D. Truncated cube
Ask by Lindsey Santiago. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The polyhedron is a quadratic pyramid.
Solution
The correct answer is C. Quadratic pyramid.
To explain briefly without the original diagram: A quadratic (i.e. square) pyramid is a polyhedron with a square base and four triangular faces meeting at an apex. In contrast, a quadratic prism (or square prism) has two parallel square bases connected by four rectangular lateral faces; a pentagonal prism has pentagonal bases and five side faces; and a truncated cube is a more complex solid (an Archimedean solid) resulting from cutting off the vertices of a cube, yielding 14 faces in total.
Based on the options given, the polyhedron showing one square face joined to four triangles (for a total of 5 faces) is best identified as a quadratic pyramid.
Thus, answer C is correct.
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Simplify this solution Extra Insights
The polyhedron in question is best identified as a pentagonal prism (B). A pentagonal prism features two parallel pentagonal bases and five rectangular faces connecting the corresponding sides of the bases. It's an intriguing solid that showcases how geometry can create complex structures using simple shapes. Polyhedra, like the pentagonal prism, appear in various fields such as architecture and art. For instance, they can be seen in the design of modern buildings with geometric facades or even in household items like boxes. Understanding shapes like the pentagonal prism helps designers think outside the box, or rather, inside the prism!
