Polyhydron
What is the meaning of Polyhydron?
A polyhedron is a three-dimensional solid whose faces are polygons.
A prism is a polyhedron that has two parallel, congruent faces called bases. The other faces are parallelograms.
A pyramid is a polyhedron whose base is a polygon and whose faces are triangles with a common vertex.
A cube is a prism whose faces are squares.
This cube has six faces, twelve edges, and eight vertices.
A pyramid is a polyhedron whose base is a polygon and whose faces are triangles with a common vertex.
This triangular pyramid has four faces, six edges, and four vertices.
This square pyramid has five faces, eight edges, and five vertices.
A cylinder is a solid whose bases are circles.
A cone is a solid with one circular base and one vertex.
A sphere is a set of all points in space that are equidistant from a given point called the center.
Polyhedra
Surface Area
The surface area of a three-dimensional figure is the sum of the areas of its faces.
Since the faces of a polyhedron are polygons, the surface area of a polyhedron is the sum of the areas of its polygonal faces.
Let’s look at a prism first.
Each of the faces of the rectangular prism below is a rectangle.
What is its surface area?
The prism has two rectangular faces with dimensions 3 in. x 8 in.
Each has area (3 in)(8 in) = 24 in
Two faces have dimensions 8 in. x 12 in.
Each has area (8 in)(12 in) = 96 in
Two faces have dimensions 3 in. x 12 in.
Each has area (3 in)(12 in) = 36 in
The surface area of the prism is:
Volume
A general formula for the volume of a prism is
V = Bh,
where B is the area of the base and h is the height.
Since volume is three-dimensional, it is expressed in cubic units,
like cubic inches (in ), cubic centimeters (cm ), and cubic feet (ft ).
Let’s look back at the prism from the previous section.
What is its volume?
The bases are any pair of congruent faces; this prism has three pairs of congruent faces. We’ll let the faces with dimensions 8 in. x 12 in. be the bases since they are on the top and bottom
(and that’s where we like our bases).
Now compute the formula for volume:
Review :
The surface area of a three-dimensional figure is the sum of the areas of its faces.
The volume of a prism is given by the formula V = Bh,
where B is the area of the base and h is the height.
The volume of a pyramid is given by the formula,
where B is the area of the base and h is the height.
