Can a polyhedron have 20 Faces, 30 Edges and 12 Vertices? Prove by Euler’s formula.
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Given : A polyhedron has 20 Faces, 30 Edges and 12 Vertices.
To find : Proof of the given statement. (using Euler's formula)
Solution :
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to prove the given statement)
Euler's formula state that :
Faces + Vertices = Edges + 2
Now, we have to put the given data in the above mentioned mathematical formula. If the given data satisfies the condition of LHS = RHS, then the given statement will be verified.
So, by putting the given data, we get :
20 + 12 = 30 + 2
32 = 32
LHS = RHS (proved)
Hence, the given statement is verified using Euler's formula.
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