Use Euler's Formula to find the number of vertices in the given polyhedron.
12 faces
2 decagons
10 rectangles
Euler's Formula states that F + V = E + 2, where F is the number of faces, V is the number of vertices, and E is the number of edges.
Given:
F = 12
2 decagons = 2 * 10 = 20 edges
10 rectangles = 10 * 4 = 40 edges
E = 20 + 40 = 60
Using Euler's Formula:
12 + V = 60 + 2
V = 60 - 12 + 2
V = 50
Therefore, the polyhedron has 50 vertices.