How many vertices does a convex polyhedron have if it has 14 faces and 24 edges? a) 8 b) 11 c) 12 d) 10

The correct answer is C) 12

Euler's formula states that the number of vertices subtracted by the number of edges and added to the number of faces of a polyhedron always equals 2:

V - E + F = 2

We have 24 edges and 14 faces:
V - 24 + 14 = 2

Combining like terms,
V - 10 = 2

Add 10 to both sides:
V - 10 + 10 = 2 + 10

V = 12

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)