Honors Geometry Section 7.3 Surface Area & Volume of Pyramids

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

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**Honors Geometry Section 7.3 Surface Area & Volume of**Pyramids**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**vertex**lateral edge lateral face base edge base**As we did with prisms, pyramids are named by the shape of**their base.**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.**The length of an altitude of a lateral face (i.e. the**altitude of a triangular face) is called the slant heightof the pyramid. altitude or height Slant height**A regular pyramid is a pyramid whose base is a regular**polygonand 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 ________.**You should always assume a pyramid is a regular pyramid**unless told otherwise.**Volume of a Pyramid = 1/3 x area of the base x the height of**the pyramid**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?**Consider a regular square pyramid whose slant height is l**and whose base edge is s.The area of each triangle ofthe net is _______The lateral area is the sum ofthe lateral faces,or ________= ________ ½ s l 4(½ sl) ½ (4s)l**Lateral Area of a Pyramid = ½ x perimeter of the base x**slant height**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.**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.**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.