Geometry B Section 12.3 Surface Area of Pyramids and Cones.

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Presentation transcript:

Geometry B Section 12.3 Surface Area of Pyramids and Cones

A pyramid is a polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex. The intersection of two lateral faces is a lateral edge. The intersection of a lateral face and the base is the base edge.

A regular pyramid has a regular polygon for its base and the vertex is straight above the center of the base. This pyramid is not regular. The slant height of a regular pyramid is the distance from the vertex to the center of a base edge.

The height or altitude of a regular pyramid is the distance from the vertex to the center of the base. The slant height of a regular pyramid is the distance from the vertex to the center of a base edge.

Theorem 12.4 Surface Area of a Regular Pyramid The surface area, S, of a regular pyramid is S = B + ½PL, where B is the area of the base, P is the perimeter of the base and L is the slant height.

A cone is a solid that has a circular base and a vertex that is not in the same plane as the base. The lateral surface consists of all segments that connect the vertex to points on the circle.

A right cone is one in which the vertex is right above the center of the base. This cone is not right.

The slant height of a right cone is the distance between the vertex and a point on the edge of the base.

Theorem 12.5 Surface Area of a Right Cone The surface area of a right cone, S, is S = πr 2 + πrL where r is the radius of the base and L is the slant height.