Question

Find the number of edges of a polyhedron having 5 vertices and 6 faces using Euler's formula​

Answer 1

⚝ Given that:-

• A polyhedron has 5 vertices and 6 faces.

⚝ To Find :-

• Number of edges ?

⚝ Solution :-

• By Euler's Formula for any polyhedron i.e,

★ F + V − E = 2 ★

Where,

• F= Faces
• V= Vertices
• E= Edges

Putting all values :-

⇢ 6 + 5 - E = 2

⇢ 11 - E = 2

⇢ E = 11 - 2

⇢ 9

Henceforth, Edges present in polyhedron = 9

Answer 2

★ Given :-

⠀⠀⠀⠀⠀⠀⠀⠀

• Number of Vertices = 5
• Number of Faces = 6

⠀⠀⠀⠀⠀⠀⠀⠀

★ To Find :-

⠀⠀⠀⠀⠀⠀⠀

• Number of Edges = ?

⠀⠀⠀⠀⠀⠀⠀

★ Solution :-

⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\maltese \: \underbrace{ \underline{\sf\pink{Using \: Euler's \: Formula}}} \\ \\ \underline{\bf{F + V - E = 2}} \\ \\ \\ \sf{6 + 5 -E = 2 } \\ \\ \sf{11 - E = 2} \\ \\ \sf{E = 11 - 2} \\ \\ \longrightarrow\boxed{\tt \red{E = 9}}$

⠀⠀⠀⠀⠀⠀⠀

★ Hence ,

⠀⠀⠀⠀⠀⠀

• The Number of Edges = 9

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