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Surface Area

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Lesson 14 Surface Area of Regular Pyramids Find the perimeter and area of each figure. Find the lateral area of a prism with a square base that is 3 cm on each side ... – PowerPoint PPT presentation

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Title: Surface Area


1
Surface Area Volume
Lesson 14
  • Surface Area of Regular Pyramids

2
Warm-Up
  • Find the perimeter and area of each figure.
  • Find the lateral area of a prism with a square
    base that is 3 cm on each side and is 7 cm tall.

16 m
16 m
16 m
5 m
11 m
11 m
3
Surface Area of Regular Pyramids
  • Target Calculate the surface area of
    regular pyramids.

4
Vocabulary
  • Slant Height (l) Height of the lateral face on
    a
  • pyramid.

5
Lateral Surface Area of a Regular Pyramid
  • The lateral area (LA) of a pyramid is equal to
    half the perimeter (P) of the base times the
    slant height (l) of the pyramid.
  • LA Pl

6
Total Surface Area of aRegular Pyramid
  • The surface area of a pyramid is equal to the sum
    of the lateral area (LA) and
  • the area of the base (B).
  • SA LA B
  • SA Pl B

7
Example 1
  • Find the surface area of the
  • regular pentagonal pyramid
  • given the base area is 139 cm2.
  • Find the perimeter of the base. 9(5) 45
  • Locate the slant height. l 12
  • Use the pyramid surface area formula. SA Pl
    B
  • Substitute known values. SA (45)(12) 139
  • Multiply, then add. SA 270 139 409
  • The surface area is 409 square centimeters.

8
Example 2
  • Find the surface area of the
  • square pyramid.
  • Find the perimeter of the base. 10.3(4) 41.2
  • Find the area of base. 10.3(10.3) 106.09
  • Locate the slant height. l 8
  • Use the surface area formula for a pyramid.
    SA Pl B
  • Substitute. SA (41.2)(8) 106.09
  • Multiply, then add. SA 164.8 106.09 270.89
  • The surface area is 270.89 square inches.

9
Exit Problems
  • Find the lateral area of a regular hexagonal
    pyramid. Each side of the base is 4 yards and
    the slant height is 3 yards.
  • Find the surface area of the pyramid.

10
Communication Prompt
  • How are the surface areas of a prisms and
    pyramids with
  • congruent bases and equal heights related?

11
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