Understanding Three Dimensional Shapes
Two dimensional shapes are flat figures. Most drawings of shapes on papers fall into the two dimensional realm. These types of shapes take up space or area, but they do not seem to have a thickness or have volume. Most representations which mankind makes of objects such as blueprints, drawings, pictures, etc… are two-dimensional representations. The surface upon which they are represented is flat. Touching the representation provides no depth, thickness or volume. Length and width can generally be calculated by examining the representation or are included as frames of reference. For example, when building a house an architect may provide a two-dimensional drawing to the perspective home owner so they have a better understanding of what the finished product will look like. However, no architect draws the house in real dimensions, a scale is included to help the home owner better understand how large the final product will be upon completion.
- Use all seven of the pieces
- They must lay flat
- They must touch another in some manner
- None of the pieces can overlap
In contrast to two-dimensional shapes, there are three-dimensional shapes. Shapes which have length, width and thickness are known as three-dimensional shapes. Examples of common three-dimensional shapes include: boxes, cans, balls, buckets, beds, etc... Returning to the example of a house and the architect from above, the architect might construct a three-dimensional miniature model of the house to further clarify specific details for the homeowner. Sometimes it is difficult for people to look at a two-dimensional drawing and imagine what the final three-dimensional product will resemble. It is in this case where models are most helpful.
Following are pictorial representations and labels for many common three-dimensional shapes.
Prisms are constructed of congruent polygons on the top and bottom, while all of the other faces are formed by rectangles. The rectangular faces are known as lateral faces while the top and bottom are referred to as bases. In the case of a rectangular prism, the faces are all rectangles, just as the cube had square faces. A rectangular prism has six faces, eight vertices and twelve edges. A refrigerator would be a real-life example of a rectangular prism.
Pyramids are polyhedrons where the base is a polygon and all of the other faces are triangles. In many pyramids, the lateral faces are also congruent. Congruent shapes are those which are the same size and shape. The vertex in a pyramid is where the lateral faces meet. It is also referred to as the apex. A triangular pyramid has a triangle for a base and three other triangular sides. It therefore has four faces, four vertices and six edges. A rectangular pyramid has a rectangle as the base with the other four faces being triangles. A rectangular pyramid has five faces, five vertices and eight edges.
The more detailed one can be when describing two- and three- dimensional shapes, the more accurate they will be represented or understood by others. The number of faces, edges and vertices on a prism or pyramid changes with the number of sides on the base.
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