Question

(a) can a polyhedron have 10 faces 20 edges and 15 vertices. (b) verify eulers formula for a right triangular prism​

Answer 1

Answer:

(a) formula can't be proved. Hence, a polyhedron can not have 10 faces,20 edges and 15 vertices.

(b)Recall the Euler's formula, F + V = E + 2 Here number of faces, F = 5 Number of vertices, V = 6 Number of edges, E = 9 Consider, F+V = 5 + 6 = 11 E + 2 = 9 + 2 = 11Hence F + V = E + 2 Thus Euler's formula is verified.

Step-by-step explanation:

Answer 2

Question 1:

can a polyhedron have 10 faces 20 edges and 15 vertices ?

Answer with explanation :

Let's try it to prove it with Euler's formula

F + V - E = 2

So, F = 10, E = 20, V = 15

= 10 + 15 - 20

= 25 - 20

= 5\ne2

Euler's formula doesn't proved,

• Hence a Polyhedron can't have 10 faces, 15 vertices and 20 edges.

Question 2:

verify eulers formula for a right triangular prism.

Answer with explanation:

Faces = 5, Edges = 9, Vertices = 6

Euler's formula =

V + F - E = 2

6 + 5 - 9 = 2

11 - 9 = 2

2 = 2

• Hence, Euler's formula verified for right triangular prism.