Question

A polyhedron has 9 faces and 14 edges. How many corners will it have?​

Answer 1

Step-by-step explanation:

By euler's formula F+V-E=2

Therefore, 9+V-14=2

9+V=2+14

9+V=16

V=16-9=7

Thus the polyhedron will have 7 corners.

Answer 2

Given :- A polyhedron has 9 faces and 14 edges.

To Find :- How many corners will it have ?

Concept used :-

• According to euler formula in a polygon :- Number of Faces + Number of Vertices - Number of Edges = 2
• Any polygon has as many corners as it has sides . So, Number of Vertices = Number of corner points .

Solution :-

Let the given polyhedron has total x vertices .

So,

→ Number of Faces + Number of Vertices - Number of Edges = 2

putting given values,

→ 9 + x - 14 = 2

→ x + 9 - 14 = 2

→ x - 5 = 2

→ x = 2 + 5

→ x = 7

then,

→ Total number of vertices of given polyhedron = 7

now,

→ Number of Vertices = Number of corner points .

therefore,

→ Number of corner points = 7 (Ans.)

Hence, the given polyhedron has total 7 corners .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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