Question

A solid has faces that consist of 4 triangles, 3 rectangles, and 1 hexagon. The solid has 9 vertices. How many edges does the solid have?

A.
12 edges
B.
15 edges
C.
18 edges
D.
21 edges

Answer 1

B. 15 edges

Explanation:

The number of edges can be found using Euler's formula for polyhedra:

Number of vertices + Number of faces - Number of edges = 2.

Given that the solid has 9 vertices, 4 triangles, 3 rectangles, and 1 hexagon, we can substitute these values into the equation:

9 + 4 + 3 + 1 - Number of edges = 2.

Simplifying this equation gives:

17 - Number of edges = 2.

Adding "Number of edges" to both sides of the equation gives:

17 = 2 + Number of edges.

Subtracting 2 from both sides of the equation gives:

Number of edges = 17 - 2 = 15.

Therefore, the solid has 15 edges.

Answer: B. 15 edges.

Answer 2

B.15

Explanation:

To find the number of edges of the solid, we can use Euler's formula, which states that the number of faces plus the number of vertices minus the number of edges equals 2.

Given that the solid has 4 triangles, 3 rectangles, and 1 hexagon as faces, the total number of faces is 4 + 3 + 1 = 8.

We are also told that the solid has 9 vertices.

Using Euler's formula, we can calculate the number of edges:

8 (number of faces) + 9 (number of vertices) - x (number of edges) = 2

Rearranging the equation, we find:

x (number of edges) = 8 + 9 - 2 = 15

Therefore, the solid has 15 edges.