Answers:
faces = 5
edges = 9
vertices = 6
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Step-by-step explanation:
Each face is a polygon representing a wall, ceiling or floor of the 3D structure. If we rotated the figure so that one triangle is flat on the ground we would have...
- 2 triangles for the floor and ceiling
- 3 rectangles for the walls
That's 2+3 = 5 faces total.
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The edges connect adjacent faces. For instance, two neighboring walls are connected with an edge. There are 3 edges that connect adjacent walls. There are 3+3 = 6 more edges that connect a wall to either the ceiling or the floor.
That's 3+6 = 9 edges total.
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Vertices are corner points. They are endpoints of segment edges.
The triangular floor provides 3 vertices. The triangular ceiling provides the other 3.
That's 3+3 = 6 vertices total
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Extra info:
Euler's polyhedron formula is
F+V-E = 2
where
- V = number of vertices
- F = number of faces
- E = number of edges
Let's use that formula for
- F = 5 faces
- V = 6 vertices
- E = 9 edges
So,
F+V-E = 2
5+6-9 = 2
11-9 = 2
2 = 2
The formula works for this polyhedron and any other polyhedron. So if you know two of the three items (say the value of F and V), you can use the formula to determine the missing third piece.