Surface Area of Regular Pyramids

Lesson 14

Find the perimeter and area of each figure.

1.

2.

3. 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

11 m

16 m

16 m

11 m

5 m

Target: Calculate the surface area of regular pyramids.

Slant Height (l) : Height of the lateral face on a 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 = Pl2

1

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 + B2

1

Find the surface area of theregular 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.

2

12

1

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.

2

12

1

1. Find the lateral area of a regular hexagonal pyramid. Each side of the base is 4 yards and the slant height is 3 yards.

2. Find the surface area of the pyramid.

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