A polyhedron has 6 faces and 4 vertices. Use Euler's formula to calculate the number of edges.
Euler said:
V + F - E = 2
so if
4 + 6 - E = 2
-E = -8
E = 8
It has 8 edges
Euler's formula states that for any polyhedron, the number of faces (F), vertices (V), and edges (E) are related by the equation F + V - E = 2.
Given that the polyhedron in question has 6 faces (F) and 4 vertices (V), we can substitute these values into the equation:
6 + 4 - E = 2
Now, let's solve for E:
10 - E = 2
Subtracting 10 from both sides:
-E = -8
Multiplying both sides by -1:
E = 8
Therefore, the polyhedron has 8 edges.
Euler's formula, named after the Swiss mathematician Leonhard Euler, relates the number of faces (F), vertices (V), and edges (E) in a polyhedron. The formula states that F + V - E = 2.
Now, to calculate the number of edges in the given polyhedron with 6 faces and 4 vertices, we can use Euler's formula. Let's substitute the values into the formula:
6 + 4 - E = 2
Simplifying the equation:
10 - E = 2
To isolate E, we subtract 10 from both sides of the equation:
-E = 2 - 10
-E = -8
Finally, we multiply both sides of the equation by -1 to find the positive value of E:
E = 8
Therefore, the polyhedron has 8 edges.