Question

find the number of faces edges and vertices of pyramid with square base verify euler's formula for it​

Answer 1

Answer:

Euler's polyhedron formula, V−E+F=2

V = number of vertices = 5

E = number of edges =?

F = number of faces = 5

Thus 5−E+5=2

⇒E=10−2

⇒E=8

Number of edges = 8

Answer 2

Given : pyramid with square base

To Find :  number of faces, edges and vertices

Verify Euler Formula

Solution:

pyramid with square base

4 vertex of Square  as base

and 1 vertex at top  

=> Total Vertex  V =  4 + 1 = 5

On Face is Square

4 faces are ( slanted ) of 4 triangles

Faces  F  = 1 + 4 = 5

Edges

4 - Edges of Square

3 Edges of one triangle hence 3 x 4 = 12 Edges

But 1 Edge of triangle is common with other triangle

and 1 Edge of triangle is common with Square

Hence 2 x 4 = 8 Edges to be reduced

Edges = 4 + 12 - 8 = 8

Vertex V = 5

Faces  F = 5

Edges  E  = 8

Euler formula for faces

= Edges - Vertex + 2

=> F = E - V + 2

LHS = F = 5

RHS = E - V + 2

= 8 -  5  + 2

= 5

LHS = RHS

Hence Verified

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