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Section 6.2

Section 6.2. Spatial Relationships. Figures in Space. Closed spatial figures are known as solids . A polyhedron is a closed spatial figure composed of polygons, called the faces of the polyhedron. The intersections of the faces are the edges of the polyhedron.

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Section 6.2

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  1. Section 6.2 Spatial Relationships

  2. Figures in Space • Closed spatial figures are known as solids. • A polyhedron is a closed spatial figure composed of polygons, called the faces of the polyhedron. • The intersections of the faces are the edges of the polyhedron. • The vertices of the faces are the vertices of the polyhedron.

  3. Polyhedrons • Below is a rectangular prism, which is a polyhedron. A B Specific Name of Solid: Rectangular Prism D C Name of Faces: ABCD (Top), EFGH (Bottom), DCGH (Front), E F ABFE (Back), AEHD (Left), H G CBFG (Right) Name of Edges: AB, BC, CD, DA, EF, FG, GH, HE, AE, BF, CG, DH Vertices: A, B, C, D, E, F, G, H

  4. Intersecting, Parallel, and Skew Lines • Below is a rectangular prism, which is a polyhedron. A B Intersecting Lines: AB and BC, BC and CD, D C CD and DA, DA and AB, AE and EF, AE and EH, BF and EF, BF and FG, CG and FG, CG and GH, DH and GH, E FDH and EH, AE and DA, AE and AB, BF and AB, BF and BC, CG and BC H G CG and DC, DH and DC, DH and AD

  5. Intersecting, Parallel, and Skew Lines • Below is a rectangular prism, which is a polyhedron. A B Parallel Lines: AB, DC, EF, and HG; D C AD, BC, EH, and FG; AE, BF, CG, and DH. E FSkew Lines: (Some Examples) AB and CG, EH and BF, DC and AE H G

  6. Formulas in Sect. 6.3 and Sect. 6.4 • Diagonal of a Right Rectangular Prism • diagonal = √(l² + w² + h²). l = length, w = width, h = height • Distance Formula in Three Dimensions • d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ + z₁)²] • Midpoint Formula in Three Dimensions • x₁ + x₂ , y₁ + y₂ , z₁ + z₂ 2 2 2

  7. Section 7.1 Surface Area and Volume

  8. Surface Area and Volume • The surface area of an object is the total area of all the exposed surfaces of the object. • The volume of a solid object is the number of nonoverlapping unit cubes that will exactly fill the interior of the figure.

  9. Surface Area and Volume Rectangular Prism Cube Surface Area S = 6s² Volume V = s³ S = Surface Area V = Volume s = side (edge) • Surface Area • S = 2ℓw + 2wh + 2ℓh • Volume • V = ℓwh • ℓ = length • w = width • h = height

  10. Section 7.2 Surface Area and Volume of Prisms

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