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. The vertices of the faces are the vertices of the polyhedron.

Polyhedrons Below is a rectangular prism, which is a polyhedron. A BSpecific Name of Solid: Rectangular Prism D CName 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

Intersecting, Parallel, and Skew Lines Below is a rectangular prism, which is a polyhedron. A BIntersecting Lines: AB and BC, BC and CD, D CCD 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 GCG and DC, DH and DC, DH and AD

Intersecting, Parallel, and Skew Lines Below is a rectangular prism, which is a polyhedron. A BParallel Lines: AB, DC, EF, and HG; D CAD, 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

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

Section 7.1 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.

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

Section 7.2 Surface Area and Volume of Prisms