geometry b section 12.3 surface area of pyramids and cones
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Geometry B
Section 12.3
Surface Area of Pyramids and Cones
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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.
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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.
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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.
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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.
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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.
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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.
![Page 8: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/8.jpg)
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.
![Page 9: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/9.jpg)
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.
![Page 10: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/10.jpg)
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.
![Page 11: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/11.jpg)
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.
![Page 12: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/12.jpg)
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.
![Page 13: Geometry B Section 12.3 Surface Area of Pyramids and Cones](https://reader036.vdocuments.site/reader036/viewer/2022081816/56649ec75503460f94bd4318/html5/thumbnails/13.jpg)
A right cone is one in which the vertex is right above the center of the base.
This cone is not right.
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The slant height of a right cone is the distance between the vertex and a point on the edge of the base.
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Theorem 12.5 Surface Area of a Right Cone
The surface area of a right cone, S, is S = πr2 + πrL where r is the radius of the base and L is the slant height.