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Geometric Solids: The Prism

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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.

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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)

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Solid Geometry Solid Geometry encompasses prisms, pyramids, cones, cylinders, and spheres.

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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.

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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

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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.

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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

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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.

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Example 1: Find the Lateral Area, Surface Area, and Volume of the Right Prism 5 4 8 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. = 144 + 2(20) = 184 sq. units The height or h = 8

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6 8 5 4 4 Perimeter of base = 6 + 5 + 8 = 19 L. A. = 19 x 4 = 76 sq. units The Base or B = ½ (6)(4) = 12 S. A. = 76 + 2(12) = 100 sq. units The height or h = 4 Example 2: Find the Volume of the Right Prism

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