Geometric Solids:
The Prism
Review of Planes
• A plane is a flat surface (think tabletop) that
extends forever in all directions.
• It is a two-dimensional (2D) figure.
• Three non-collinear points determine a plane.
• So far, all of the geometry we’ve done takes
place in a plane.
• But objects in the real world are threedimensional, so we will have to leave the plane
and talk about objects like spheres, cubes,
cones, and cylinders.
2
Solid Geometry
Solid Geometry is the geometry of three-dimensional
space, the kind of space we live in ...
Solid Geometry has Three Dimensions.
It is called three-dimensional, or 3D
because there are three dimensions:
width, depth and height.
Properties
Solids have properties (special things
about them), such as:
Volume (think of how much water it
could hold)
Surface area (think of the area you
would have to paint)
Solid Geometry
Solid Geometry encompasses prisms, pyramids,
cones, cylinders, and spheres.
Our First Solid: The Prism
• Prisms: A solid that is formed by parallelograms.
• The two shaded faces of the prisms are the
bases.
• The other faces of a prism that are NOT bases
are called lateral faces.
• Adjacent lateral faces interest in parallel
segments called lateral edges.
• An altitude of a prism is a segment that joins
the two bases and is perpendicular to both.
• The length of an altitude is the height, h, of
the prism.
Formulas for Prism Area
o
The Surface Area is measured in square units.
o
o
The Lateral Area of a prism is the sum of the
areas of its lateral faces.
o
o
Surface Area: S.A. = ph + 2B (B = area of base)
Lateral Area: L.A. = ph (p = perimeter, h =
height)
The Total Area is the sum of the areas of all of
the faces
o
Total Area: T.A. = L.A. + 2B
Formulas for Prism Volume
• Prisms have volume as well as area.
• A rectangular solid with square faces is a cube.
• Volume – Volume is measured in cubic units. The
volume of a right prism equals length x width x
height or V=lwh. Since Base = length x width, then
V = Bh.
Right Prism vs. Oblique
Prism
Right Prism – A prism which has bases
aligned one directly above the other and has
lateral faces that are rectangles.
Oblique Prism - A prism with bases that are
not aligned one directly above the other. Note:
The lateral faces of an oblique prism are
parallelograms.
Right Prism vs. Oblique
Prism
Right
Square
Prism
Right
Triangular
Prism
Right
Pentagonal
Prism
Oblique
Square
Prism
** The Prisms are named by their base, square, triangle, pentagon,
square. The Right or Oblique refers to the lateral faces.
Example 1: Find the Lateral Area,
Surface Area, and Volume of the
Right Prism
8
5
4
Perimeter of base = 2(5) + 2(4) = 18
L. A.= 18 x 8 = 144 sq. units
S.A. = 144 + 2(20) = 184 sq. units
The height or h = 8
The base or B = 5 x 4 = 20
V = 20 x 8 = 160 cubic units
Example 2: Find the Volume of
the Right Prism
4
8
L. A. = 19 x 4 = 76 sq. units
4
6
Perimeter of base = 6 + 5 + 8 = 19
5
S. A. = 76 + 2(12) = 100 sq. units
V = 12 x 4 = 48 cubic units
The height or h = 4
The Base or B = ½ (6)(4) = 12