2 DefinitionsPrism – polyhedron with 2 faces (called bases) that lie in planes.Named by the shape of the bases.Lateral Faces – the faces that are NOT bases (all are ’ogram shaped)Lateral Edges – edges of the lateral faces that are NOT edges of the bases as well.Height (altitude) - distance between the bases.Right Prism – lateral edges are to bases.Oblique Prism – lateral edges are NOT to the bases. (looks slanted)
4 3-D AreasLateral Area (LA) – the sum of the areas of the lateral faces only.Does not include the area of the bases.Surface Area (S) – the sum of the areas of ALL the faces.Lateral area + area of the bases
5 Net Defn. – a 2-dimensional representation of a solid. Just think “unfold” the figure and lay it flat.Ex:
6 To find surface or lateral areas, you could find the areas of each individual face and then add them all together; OR you could use formulas!Thm 12.2 – SA of a rt. PrismS = 2B + PhB = area of base, P = perimeter of base, h = height of prismWhat about Lateral Area?* remember: LA is everything BUT the bases!So, LA = Ph
7 Ex: Find the lateral & surface areas of the triangular prism. LA = PhP = 6*3 = 18LA = 18*10LA = 180 in2S = 2B + PhS = 2(15.59) + 180S =S = in26 in.60o10 in.
8 Cylinder Defn. – solid with , circular bases. Can be oblique or right.Lateral Area – the area of the curved surface.What does the curved surface look like if laid out flat?Think of the label of a soup can!It’s a rectangle! (area of rectangle = bh)Surface Area – lateral area + area of bases.hh
9 Let’s look at lateral area 1st! Thm 12.3: SA of a rt. cylinderLet’s look at lateral area 1st!LA = ChorLA = 2rhSo, S = 2B + ChS = 2r2 + 2rh
10 Ex: Find the lateral & surface areas of the cylinder. LA = 2rhLA = 2(4)(8)LA = 64 m2Or m2S = 2r2 + 2rhS = 2(42) + 64S = 32 + 64S = 96 m2Or m24 m.8 m.