Geometric Solids: The Prism

2 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 three- dimensional, so we will have to leave the plane and talk about objects like spheres, cubes, cones, and cylinders.

Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in...geometry 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 Surface Area: S.A. = ph + 2B (B = area of base) o The Lateral Area of a prism is the sum of the areas of its lateral faces. o Lateral Area: L.A. = ph (p = perimeter, h = height) o 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 – 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. bases lateral facesrectanglesprismbaseslateral faces parallelogramsbases lateral facesrectanglesprismbaseslateral faces 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 Perimeter of base = 2(5) + 2(4) = 18 The base or B = 5 x 4 = 20 L. A.= 18 x 8 = 144 sq. units S.A. = (20) = 184 sq. units The height or h = 8

Perimeter of base = = 19 L. A. = 19 x 4 = 76 sq. units The Base or B = ½ (6)(4) = 12 S. A. = (12) = 100 sq. units The height or h = 4 Example 2: Find the Volume of the Right Prism