Question

Using Euler's formula, find V, if E = 30, F= 12. If the solid figure is a prism, then how many sides the base polygon has?

Answer 1

Given:
E = 30 and F = 12
According to Euler’s formula,
V $-$ E + F = 2
$\Rightarrow$V $-$ 30 + 12 = 2
$\Rightarrow$V = 20
We know that there are equal vertices at the top and bottom of the prism.
∴ Number of vertices at the bottom = $\frac{V}{2}=\frac{20}{2}=10$
Also,
We know that number of sides is equal to the number of vertices.
∴ Number of sides of the base polygon = 10