11.3 Surface Areas of Pyramids and Cones

11.3 Surface Areas of Pyramids and Cones A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid). Pyramids The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base.

The length of the altitude is the height of the pyramid. A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. The slant height is the length of the altitude of a lateral face of the pyramid. Lateral and Surface Areas of a Pyramid 1 L. A. P

2 S . A. L. A. B Cones A cone is a solid that has one base and a vertex that is not in the same plane as the base. The base of a cone is a circle. In a right cone, the altitude is the perpendicular segment from the vertex to the center of the base. The height, h, is the length of the altitude.

The slant height, , is the distance from the vertex to a point on the edge of the base. Surface Area of a Cone S . A. L. A. B S . A. r r 2 (15)(25) (15)

375 225 2 600 cm 2

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