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Warm-Ups
12.1 Three-Dimensional Figures
Polyhedron:
a solid with all flat surfaces that enclose a single region of space.
-Face: each flat surface -Edge: line segments where faces intersect -Vertices: edges intersect at points Regular Polyhedron: all faces are regular congruent polygons and all edges are congruent.
Prism :
a polyhedron with two parallel congruent face called bases; all other faces are parallelograms.
* Prisms are named by the shape of their bases.
Regular Prism: a prism with bases that are regular polygons.
COMMON PRISMS:
Pyramid:
polyhedron with all faces (except one) intersecting at a vertex. (ex: pyramids hanging in classroom)
* Pyramids are named by their bases.
Platonic Solids:
exactly five types of regular polyhedra
.
(hexahedron)
Solids that are not polygons:
Identify the solid. Name the bases, faces, edges, and vertices.
The bases are rectangles, and the four remaining faces are parallelograms.
Answer:
This solid is a rectangular prism.
Bases: Faces: Edges: Vertices:
A, B, C, D, E, F, G, H
Identify the solid. Name the bases, faces, edges, and vertices.
The bases are circular and congruent.
Answer:
This solid is a cylinder.
Bases:
Identify the solid. Name the bases, faces, edges, and vertices.
The base is a triangle, and the remaining three faces meet at a point.
Answer:
This solid is a triangular pyramid.
Base: Faces: Edges: Vertices:
A, B, C, D
a.
Identify the solid. Name the bases, faces, edges, and vertices.
Answer:
triangular prism
Bases: Faces: Edges: Vertices:
A, B, C, E, F, G
b.
Identify the solid. Name the bases, faces, edges, and vertices.
Answer:
cylinder
Bases:
c.
Identify the solid. Name the bases, faces, edges, and vertices.
Answer:
pentagonal pyramid
Bases:
ABCDE
Faces: Edges: Vertices:
A, B, C, D, E, F
BAKERY A customer ordered a two-layer sheet cake. Describe the possible cross sections of the cake.
Answer:
If the cake is cut horizontally, the cross section will be a rectangle.
If the cake is cut vertically, the cross section will also be a rectangle.
A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints of a circle, triangle, and an oval?
Answer:
If the cone were to be cut parallel to the base, the cross-section would be a circle.
Answer:
If the cone were to be cut perpendicular to the base, the slice would be a triangle.
If the cone were to be cut on an angle to the base, the slice would be an oval.