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Verify whether the above hold true for Euler’s formula for Platonic Solid. Now, let’s work out a few
examples based on the Euler’s Formula.

Example 2: If a polyhedron has 5 faces and 6 vertices,
find the number of edges. Think and Answer

Solution: Here, F = 5 and V = 6, then E = ? 1. Triangular pyramid is also called .......... .
2. A pentagonal prism has .......... faces.
We have, F + V = E + 2
3. A solid shape having 5 faces, 5 vertices
⇒ 5 + 6 = E + 2 and 8 edges is ...........

⇒ 11 = E + 2 4. A triangular prism has .......... lateral faces.
5. Is square prism same as a cube?
⇒ E = 11 – 2 = 9

So, the number of edges, E = 9.
Example 3: If a polyhedron has 24 edges and 16 vertices, find the number of faces.
Solution: Here, E = 24 and V = 16, then F = ?

We have, F + V = E + 2
⇒ F + 16 = 24 + 2

⇒ F + 16 = 26 ⇒ F = 26 – 16 = 10
So, the number of faces, F = 10.

Maths Talk
1. How are prisms and cylinders alike? Discuss with your teacher and classmates.
2. How are pyramids and cones alike? Discuss with your teacher and classmates.

Practice Time 9C

1. Find the number of faces, edges and vertices of the following solids. Also verify Euler’s formula.
(a) Cuboid (b) Triangular prism (c) Square pyramid
(d) Rectangular prism (e) Pentagonal pyramid (f) Pentagonal prism

2. Using Euler’s formula, find the unknown.

(a) (b) (c) (d)
Faces 4 6 20 ?

Vertices ? 8 12 6

Edges 8 ? ? 12
3. Can a polyhedron have 10 faces, 20 edges and 15 vertices?

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