Question

Find the number of vertices in a polyhedron which has 30 edges and 12 faces

Answer 1

As per the Euler's formula, Faces + Vertices = Edges +2
Let vertices = x


12+x= 30+2
12+x=32
x=32-12
x=20

Therefore...the number of vertices =20


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Answer 2

Given,

• Number of edges = 30
• Number of faces = 12

To find,

• The number of vertices in a polyhedron.

Solution,

The number of vertices in a polyhedron that has 30 edges and 12 faces are 20.

We can simply find the number of vertices in a polyhedron by using Euler's formula,

                F + V = E + 2

in which, F is the face of a polyhedron, V is the vertices of a polyhedron, and E is the edges of a polyhedron.

Substituting the given values in the formula for finding the vertices, we get

                 12 + V = 30 +2

                 12 + V = 32

                         V = 32-12

                        V = 20

∴ The vertices of a polyhedron are 20.

Hence, the number of vertices in a polyhedron that has 30 edges and 12 faces are 20.