To find the surface area of a pyramid, you must ... lateral surface of a pyramid is
the area of the lateral faces (not including the base). ... Use the formula. SA r2.
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11-5 Surface Area: Pyramids and
Cones
(Pages 578–582)
A pyramid is a solid figure that has a polygon for a base and triangles for sides, or lateral faces. Pyramids have just one base. The lateral faces intersect at a point called the vertex. Pyramids are named for the shapes of their bases. For example, a triangular pyramid has a triangle for a base. A square pyramid has a square for a base. The slant height of a pyramid is the altitude of any of the lateral faces of the pyramid. To find the surface area of a pyramid, you must find the area of the base and the area of each lateral face. The area of the lateral surface of a pyramid is the area of the lateral faces (not including the base). A circular cone is another solid figure and is shaped like some ice cream cones. Circular cones have a circle for their base. Surface Area of a Circular Cone
Examples
The surface area of a cone is equal to the area of the base, plus the lateral area of the cone. The surface area of the base is equal to r 2. The lateral area is equal to r, where is the slant height of the cone. So, the surface area of the cone, SA, is equal to r 2 r.
Find the surface area of the given geometric solids.
a. a square pyramid with a base that is 20 m on each side and a slant height of 40 m
b. a cone with a radius of 4 cm and a slant height of 12 cm Use the formula. SA r2 r SA (4)2 (4)(12) SA 50.3 150.8 SA 201.1 cm2
Find the surface area of the base and the lateral faces. Base: Each triangular side: 1 2
1 2
A s2 or (20)2
A bh or (20)(40)
A 400 SA 400 4(400) SA 2000 m2
A 400 Area of the base plus area of the four lateral sides.
Practice Find the surface area of each solid. Round to the nearest tenth. 1.
2.
3.
18.2 m 28.7 ft 10 ft
10 m
4.
12.3 mm
5.
11.4 in.
8 mm
10 ft
8 mm
6. 21 cm 3.1 in.
15.3 in.
2.2 in.
2.2 in.
17 cm
7. Standardized Test Practice What is the surface area of a square pyramid where the length of each side of the base is 10 meters and the slant height is also 10 meters? A 300 m2 B 400 m2 C 500 m2 D 1000 m2
