Surface Area and Volume of Pyramids Section 10-5 and 10-7 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Definitions A polyhedron is a pyramid if and only if it has one base and its lateral faces are triangles with a common vertex. Regular Pyramid is one whose base is a regular polygon. Slant height is the height of one of the congruent lateral faces. A cone is a 3-D figure with one circular base and a vertex not on the same plane as the base. Altitude is a perpendicular segment connecting vertex to the plane containing the base . Slant height is the segment connecting vertex to the circular edge of the base 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids

Area and Volume Formulas for Pyramids Lateral Area of a Regular Pyramid: LSA = (1/2)Pl where P is the perimeter and l is slant height Surface Area of a Regular Pyramid: S = (1/2)Pl + B where B is the base area Volume of a Pyramid: V = 1/3 Bh where B is the Base’s Area and h is height 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Example 1 Find the lateral area and surface area of a regular square pyramid with base edge length 14 cm and slant height 25 cm. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Example 2 Find the lateral and total surface area of the regular pyramid. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Example 2 Find the lateral and total surface area of the regular pyramid. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Your Turn Find the lateral area and surface area of a regular triangular pyramid with base edge length 6 ft and slant height 10 ft. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Example 3 Find the volume of the square pyramid with base edge length 9 cm and height 14 cm. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Example 4 Find the volume of the regular hexagonal pyramid with height equal to the apothem of the base. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Your Turn Find the volume of the regular hexagonal pyramid with height equal to the apothem of the base. 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids

10-5: Surface Area of Pyramids Assignment Worksheet 1/17/2019 4:20 AM 10-5: Surface Area of Pyramids