Aconvex polyhedron has faces that consist of 6 octagons, 8 hexagons, and 12 squares. the polyhedron has 48 vertices. how many edges does it have?

euler’s formula: v + f = e + 2

24
26
72
74

Option C is correct.

Step-by-step explanation:

We are given Euler's Formula,

V + F = E + 2

where V = number of vertex

           F = Number of faces

           E = Number of Edges

Convex polyhedron has 6 octagons , 8 hexagons and 12 square as faces.

⇒ Number of faces , F = 6 + 8 + 12 = 26

Number of vertices , V = 48

We have to find : Number of edges.

Using Euler's formula,

48 + 26 = E + 2

E = 74 - 2

E = 72

Therefore, Option C is correct.

step-by-step explanation:

consider the parallelogram shown in the attached image.

in the parallelogram hijk, the length of hk is given as,

from the properties of parallelogram we know that the opposite sides of a parallelogram are parallel to each other and are equal in measure.

therefore, the length of the side ij must be equal to the length of the side hk and that is .

hence, the expression for the length of ij confirms that hijk is a parallelogram.