Use Euler’s formula to answer question.A polyhedrons has 20 vertices and 20 faces. How many edges does it have?Options are-42-40-38-39

Accepted Solution

Answer:  The correct option is (C) 38.Step-by-step explanation:  Given that a polyhedron has 20 vertices and 20 faces.We are to find the number of edges of the polyhedron using Euler's formula.Euler's formula :For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.For the given polyhedron, we havenumber of vertices, V = 20,number of faces, F = 20andnumber of edges, E = ?Therefore, from Euler's formula[tex]V-E+F=2\\\\\Rightarrow 20-E+20=2\\\\\Rightarrow 40-E=2\\\\\Rightarrow E=40-2\\\\\Rightarrow E=38.[/tex].Thus, the required number of edges of the given polyhedron is 38.Option (C) is CORRECT.