Question

Question

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An illustration shows a composite figure of two similar sets where a central pentagon is surrounded by a layer of 5 pentagons, one on each side. Two central pentagons are drawn separately with dashed lines. On each side of the central pentagons, another pentagon is drawn using solid lines. Each central pentagon has 5 surrounding pentagons. One pentagon from each set shares a common side.

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?

(1 point)
Responses

60 triangles and 0 trapezoids
60 triangles and 0 trapezoids

6 triangles and 6 trapezoids
6 triangles and 6 trapezoids

12 triangles and 12 trapezoids
12 triangles and 12 trapezoids

10 triangles and 10 trapezoids
10 triangles and 10 trapezoids
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Answer 1

To determine how many triangles and trapezoids can be formed from the given pentagons in the dodecahedron, let's analyze the properties of a dodecahedron and the decomposition of pentagons.

A dodecahedron consists of 12 pentagonal faces. If we decompose each pentagon into one triangle and one trapezoid, we can perform the following calculation:

• Each of the 12 pentagons can be divided into:
  • 1 triangle
  • 1 trapezoid

Therefore, for 12 pentagons:

• Total triangles = 12 (1 triangle from each pentagon)
• Total trapezoids = 12 (1 trapezoid from each pentagon)

Thus, the total numbers are:

• 12 triangles
• 12 trapezoids

The correct answer is: 12 triangles and 12 trapezoids.