Question

Mario’s company makes unusually shaped imitation gemstones. One gemstone has 10 faces and 12 vertices. How many edges does the gemstone have?

Answer 1

20 edges
F=12, V=10
V -E+F=2
10-E+12=2
-E+22=2
-E=-20
E=20

Answer 2

Answer: The gemstone has 20 edges.

Step-by-step explanation: We are given that Mario’s com pany makes unusually shaped imitation gemstones. One gemstone has 10 faces and 12 vertices.

We are to find the number of edges that the gemstone have.

Euler's formula : If F, E and V represents the number of faces, number of edges and number of vertices respectively, then the following is true :

`F+V-E=2~~~~~~~~~~~~~~~~~~~~~~~~(i)`

For the given gemstone, we have

F = 10, V = 12 and E = ?

From equation (i), we get

`F+V-E=2\\\\\Rightarrow 10+12-E=2\\\\\Rightarrow 22-2=E\\\\\Rightarrow E=20.`

Thus, the gemstone has 20 edges.