1. Surface Area of Regular Pyramids
Lesson 14
Surface Area & Volume
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 a Regular 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 = = 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 (4) = 41.2
Find the area of base (10.3) =
Locate the slant height l = 8
Use the surface area formula for a pyramid SA = Pl + B
Substitute. SA = (41.2)(8)
Multiply, then add. SA = =
The surface area is 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?