12.3 Surface Area of Pyramids and Cones

State Standards8, 9: Solve problems involving

the surface area lateral area of geometric solids and COMMIT TO MEMORY THE NECESSARY FORMULAS.

Lesson Goals• Find the surface area of a

pyramid

definitions• Pyramid

– Base: a polygon– Lateral faces: triangles around the perimeter of the base with a common vertex.– Altitude: the perpendicular distance between the base and the vertex.– A pyramid is named for its base.

Rectangular Pyramid Hexagonal Pyramid

definitionsPyramid Regular: the base is a regular polygon Slant height: the altitude of any lateral face. A non-regular pyramid does not have a defined slant height.

lateral face

slant height

taking the stairsaltitudetaking the elevator

SURFACE AREA (PYRAMID)

base lateral facesA A

Find the area of a lateral face and the surface area. Round the result to one decimal place. 1 6 9

2lateral faceA

36 4 27SA

Find the surface area. Round the result to one decimal place.

4

164 32 4 102

S

Find the area of a lateral face and the surface area. Round the result to one decimal place.

164 32 4 102

S

Find the missing measurements of the regular right pyramid.

exampleFind the surface area.

126hexagonA sa

2 3a

24 3hexagonA

1224 3 6( 4 9)SA

4 ft

9 ft

22 149.6 ft24 3 108 ftSA

126 4 2 3hexagonA

You try 126hexagonA sa

6 3hexagonA

221

26 3 6 2 5 3SA

22 42.14 ft6 3 12 7 ftSA

126 2 1 3hexagonA

3cm

5cm 2

25 3 126 3 6 2 2 7SA

Today’s Assignmentp. 738: 3 – 7, 14 – 19, 26, 35, 38