7th Grade Math

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Surface Area

PART A B CDE F

Multi-Part

Lesson 2

Addresses

GLE 0706.1.7, GLE 0706.1.8.

582 Volume and Surface Area

Surface Area of Prisms

Use the cubes to build a rectangular prism with

a length of 8 centimeters. Count the number of

squares on the outside of the prism. The sum is the surface area.

1. Record the dimensions, volume, and surface area in a table.


2. Build two more prisms using 8 cubes. For each, record the
   dimensions, volume, and surface area.


3. Describe the prisms with the greatest and least surface areas.

The sum of the areas of all the surfaces, or faces, of a three-dimensional

figure is the surface area.

Surface Area of a Rectangular Prism

Words The surface area S.A. of a

rectangular prism with base ,

width w, and height h is the

sum of the areas of its faces.

Model

w



h

Symbols S.A. = 2 h + 2 w + 2 hw

Surface Area of Rectangular Prisms

Find the surface area of the

4 cm

top

front

side bottom side

back

3 cm

5 cm

5 cm

5 cm

4 cm

3 cm

4 cm

3 cm 3 cm

4 cm

rectangular prism.

There are three pairs of congruent faces.

• top and bottom


• front and back


• two sides
  Faces Area
  top and bottom 2(5 · 4) = 40
  front and back 2(5 · 3) = 30
  two sides 2(3 · 4) = 24
  sum of the areas 40 + 30 + 24 = 94
  The surface area is 94 square centimeters.

Main Idea

Find the surface areas

of prisms.

Vocabulary

surface area

V

s

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