6th Grade Math Textbook, Fundamentals

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11-4

Key Concept

Surface Area (S) of a Pyramid

S B LA, where Ssurface area,

Barea of the base, and LAlateral area.

Update your skills. See page 408 III.

Surface Area of Pyramids

Objective To draw and use nets to find the surface area of a rectangular pyramid or a triangular

pyramid • To use formulas to find the surface area of a rectangular pyramid or a triangular pyramid

• To rename surface area units in equivalent forms

Veronica is designing a three-dimensional wooden
model of a rectangular pyramid. She will cut out each
face from a thin sheet of wood and glue the edges of
the faces together. The dimensions of the model are
shown at the right. How many square centimeters of
wood will she use?

To find the amount of wood Veronica will use, find
the surface area of the model rectangular pyramid.

To find the surface area, you need to know the parts of a

triangular pyramid. The triangular sides of a pyramid are

called. The height of each lateral face is called

the. The sum of the areas of the lateral faces is

the. The

is the sum of the lateral area and the area of the base.

To find the surface area of the model rectangular pyramid,

find the area of the base and each lateral face. Then add the

areas to find the total surface area. Use a net to help.

Area of the rectangular base:

Aw 30 • 12 360 cm^2

Area of each blue triangular lateral face:

A bh (12)(17) 102 cm^2

Area of each yellow triangular lateral face:

A  bh (30)(10) 150 cm^2

Lateral area Sum of the areas of the lateral faces

2(102) 2(150) 504 cm^2

Surface areaarea of the base lateral area

 360  504 864 cm^2

So Veronica will use 864 square centimeters of wood.

1

2

1

2

1

2

1

2

lateral area of a pyramid surface area of a pyramid

slant height

lateral faces

10 cm

17 cm

12 cm

30 cm

17 cm 10 cm

12 cm

30 cm

Parts of a Pyramid

The slant heightis the height

of the triangular face notthe

height of the pyramid.

base

slant

lateral face height