Question

Find the number of faces, edges and vertices of pyramid with square base. Verify

Euler’s formula for it.​

Answer 1

Answer:

Step-by-step explanation:

Answer:

By visualising or seeing an image, u will find that it has 5 vertices,5 faces and 8 edges.

Verification

V-E+F=2

LHS

V-E+F=2

5-8+5=2

(5+5)-8=2 [Associative ppty]

2=2=RHS

Hence verified

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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