Please help me. What type of polygon would a peice of an icosahedron at a vertex create? Explain why.

Regular Pentagon

Step-by-step explanation:

A regular icosahedron is a twenty-faced polyhedron, each face being an equiangular triangle.  Each vertex is joined together by 5 faces, therefore the polygon formed at each vertex is a regular pentagon.

We can also figure out the number of faces at each vertex using Euler's formula

F+V=E+2

F=number of faces = 20

E=number of edges = number of triangular faces * edges/triangle /2

(since each edge is shared between two faces)

= 20*3/2

=30

Number of vertices

= E+2-F = 30+2-20 = 12

So number of edges meeting at each vertex

= 30 / (12/2) = 30/6 = 5

(12/2 because each edge joins two vertices).

See attached figure, courtesy of Wikipedia.

i'm not sure i quite understand, could you provide more information?

12cm

the answer is d