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
A.
12 edges
B.
15 edges
C.
18 edges
D.
21 edges
Answers
GPT 3.5
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.
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.