Presentation on theme: "Honors Geometry Section 7.3 Surface Area & Volume of Pyramids"— Presentation transcript:
1 Honors Geometry Section 7.3 Surface Area & Volume of Pyramids
2 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
4 As we did with prisms, pyramids are named by the shape of their base.
5 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.
6 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.altitudeorheightSlantheight
7 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 ________.
8 You should always assume a pyramid is a regular pyramid unless told otherwise.
9 Volume of a Pyramid = 1/3 x area of the base x the height of the pyramid
10 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?
11 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 l4(½ sl)½ (4s)l
12 Lateral Area of a Pyramid = ½ x perimeter of the base x slant height
13 Surface Area of a Pyramid = lateral area + area of the base
14 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.
15 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.
16 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.