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**Honors Geometry Section 7.3 Surface Area & Volume of Pyramids**

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A pyramid is a 3-dimensional object consisting of 1 base, which must be a polygon, and three or more lateral faces which are triangles. The lateral faces share a single vertex called the ______ of the pyramid. Base edge and lateral edge are defined in the same way they were for prisms. vertex

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vertex lateral edge lateral face base edge base

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**As we did with prisms, pyramids are named by the shape of their base.**

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The altitude of a pyramid is the segment from the vertex perpendicular to the base. The height of the pyramid is the length of the altitude.

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**The length of an altitude of a lateral face (i. e**

The length of an altitude of a lateral face (i.e. the altitude of a triangular face) is called the slant height of the pyramid. altitude or height Slant height

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A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. In a regular pyramid the altitude intersects the base at its ______ and the slant height intersects the base edge at its ________.

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**You should always assume a pyramid is a regular pyramid unless told otherwise.**

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**Volume of a Pyramid = 1/3 x area of the base x the height of the pyramid**

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Example 1: The pyramid of Khufu is a regular square pyramid with a base edge of 776 feet and a height of 481 feet. What is the volume of the pyramid?

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Consider a regular square pyramid whose slant height is l and whose base edge is s. The area of each triangle of the net is _______ The lateral area is the sum of the lateral faces, or ________= ________ ½ s l 4(½ sl) ½ (4s)l

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**Lateral Area of a Pyramid = ½ x perimeter of the base x slant height**

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**Surface Area of a Pyramid = lateral area + area of the base**

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Example 2: The roof of a gazebo is a regular octagonal pyramid with a base edge of 4 feet and a slant height of 6 feet. Find the area of the roof.

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Example 3: A regular square pyramid has base edges of 8 m and an altitude of 8 m. Find the surface area and volume of the pyramid.

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Example 3: A regular square pyramid has base edges of 8 m and an altitude of 8 m. Find the surface area and volume of the pyramid.

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