1. Surface Area and Volume of Pyramids
Section 10-5 and 10-7
Geometry PreAP, Revised ©2014
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10-5: Surface Area of Pyramids

2. 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
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10-5: Surface Area of Pyramids

3. 10-5: Surface Area of Pyramids

4. 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
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10-5: Surface Area of Pyramids

5. 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.
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10-5: Surface Area of Pyramids

6. 10-5: Surface Area of Pyramids
Example 2
Find the lateral and total surface area of the regular pyramid.
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10-5: Surface Area of Pyramids

7. 10-5: Surface Area of Pyramids
Example 2
Find the lateral and total surface area of the regular pyramid.
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10-5: Surface Area of Pyramids

8. 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.
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10-5: Surface Area of Pyramids

9. 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.
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10-5: Surface Area of Pyramids

10. 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.
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10-5: Surface Area of Pyramids

11. 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.
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10-5: Surface Area of Pyramids

12. 10-5: Surface Area of Pyramids
Assignment
Worksheet
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10-5: Surface Area of Pyramids