Question

Count the number of faces, vertices, and edges of given polyhedra and verify Euler's formula.​

Answer 1

20 is the answer

Step-by-step explanation:

1.Here,

No. of Faces (F):5  

No. of Vertices (V):6  

No. of Edges (E):9  

Euler’s formula: F + V = E + 2  

⇒ 5 + 6 = 9 + 2  

⇒ 11 = 11  

∴ Euler’s formula satisfies for the shape.

2.Here,  

No. of Faces (F):7  

No. of Vertices (V):10  

No. of Edges (E):15  

Euler’s formula: F + V = E + 2  

⇒ 7 + 10 = 15 + 2  

⇒ 17 = 17  

∴ Euler’s formula satisfies for the shape.

3.Here,  

No. of Faces (F):8  

No. of Vertices (V):12  

No. of Edges (E):18  

Euler’s formula: F + V = E + 2  

⇒ 8 + 12 = 18 + 2  

⇒ 20 = 20  

∴ Euler’s formula satisfies for the shape.

4.Here,  

No. of Faces (F):6  

No. of Vertices (V):6  

No. of Edges (E):10  

Euler’s formula: F + V = E + 2  

⇒ 6 + 6 = 10 + 2  

⇒ 12 = 12  

∴ Euler’s formula satisfies for the shape.

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