3 Prior KnowledgeA polyhedron is a three – dimensional figure, whose surfaces are polygons. Each polygon is a face of the polyhedronAn edge Is a segment that is formed by the intersection of two faces.A vertex is a point where three of more edges intersect
4 PrismA Prism is a polyhedron with two congruent parallel faces, called bases. The other faces are lateral faces.You name a prism using the shape of the baseThe altitude of a prism is the perpendicular segment that joins the planes of the bases, the height is the length of the altitude.
5 Oblique vs. RightIn a right prism the lateral faces are rectangles, and the altitude is a lateral edge. In an oblique prism some of the lateral faces are non-rectangular, * in this class you can assume that all prisms are right unless otherwise stated
6 Lateral Area Vs Surface Area Lateral Area (LA) is the sum of the areas of the lateral facesSurface Area (SA) is the sum of the lateral area and the area of the two bases
7 Formulas LA = ph SA = (LA) + 2B Where p is the perimeter of the bases and h is the height of the prismSA = (LA) + 2BWhere LA is the lateral area and B is the area of the Base
10 CylinderA cylinder is a solid that has two congruent // bases that are circlesAn altitude of a cylinder is a perpendicular segment that joins the planes of the bases.The height (h) of a cylinder is the length of the altitude
11 Oblique vs. RightIn a right cylinder the segment joining the centers of the bases is an altitudeIn an oblique cylinder the segment joining the centers in not perpendicular to the planes containing the base.* in this class you can assume that all prisms are right unless otherwise stated
12 Formulas LA = 2πrh or LA = πdh SA = LA + 2B or SA = 2πrh + 2πr2 Where r is the radius andh is the heightSA = LA + 2B or SA = 2πrh + 2πr2Where LA is the lateral area, B is the area of the base, r is the radius and h is the height
13 Example 1Find the Lateral Area and Surface Area
25 PyramidA pyramid is a polyhedron in which one face, the base, can be any polygon and the other faces, lateral faces, are triangles that meet at a common vertex called the vertex of the pyramidThe altitude of a pyramid is a perpendicular segment from the vertex of the pyramid to the plane of the base – the length of the altitude = height
26 Regular PyramidA pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.The slant height, l , is the length of the altitude of a lateral face of the pyramid.(In this class all pyramids are regular unless otherwise stated)
27 Formulas For Pyramids LA = ½ p l SA = LA + B Where p is the perimeter of the base and l is the slant height of the pyramidSA = LA + BWhere B is the area of the base of the pyramid
28 Example 1A square pyramid has base edges of 5 m and a slant height of 3 m. What is the surface area of the pyramid?
31 ConeA cone is a solid that has one base and a vertex that is not in the same plane as the baseThe base of a cone in a circleIn a right cone the altitude is aperpendicular segment from thevertex to the center of the base, the height = lengthof the altitudeThe slant height l is the distance from the vertex to a point on the edge of the base
32 Formulas For Cones LA = ½ 2πrl or LA = πrl SA = LA + B Where r is the radius, and l is the slant heightSA = LA + BWhere is B is the area of the base
33 Example 1The radius of the base of a cone is 16 m. Its slant height is 28 m. What is the surface area in terms of π?