A net that folds into a dodecahedron is made up of pentagons. If you decompose each pentagon into one triangle and one trapezoid, how many triangles and how many trapezoids are there?

Question

(1 point)
Responses

6 triangles and 6 trapezoids
6 triangles and 6 trapezoids

60 triangles and 0 trapezoids
60 triangles and 0 trapezoids

12 triangles and 12 trapezoids
12 triangles and 12 trapezoids

10 triangles and 10 trapezoids

Answer 1

A dodecahedron is a polyhedron with 12 faces, each of which is a regular pentagon. If we decompose each pentagon into one triangle and one trapezoid, we need to calculate the total number of triangles and trapezoids generated from the decomposition of all the pentagons.

1. Each pentagon can be decomposed into 1 triangle and 1 trapezoid.

2. Since there are 12 pentagons in a dodecahedron, if we apply the decomposition to each one:

   • Number of triangles = 12 (from 1 triangle per pentagon × 12 pentagons)
   • Number of trapezoids = 12 (from 1 trapezoid per pentagon × 12 pentagons)

Therefore, the answer is:

12 triangles and 12 trapezoids.