7th Grade Math

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Surface Area

PART A BCDE F

Multi-Part

Lesson 2

Addresses

GLE 0706.1.8.

594 Volume and Surface Area

Main Idea

Find the surface area

of pyramids.

Vocabulary

slant height

lateral surface area

Surface Area of Pyramids

• Copy the following net of a square
  pyramid onto a piece of paper.


• Cut out the net and tape it together.

1. What shapes make up the net of the
   square pyramid?


2. What do you notice about the
   triangular faces of the pyramid?

A right square pyramid has a square base and four isosceles triangles

that make up the lateral faces. The height of each lateral face is called

the slant height. The lateral surface area of a solid is the sum of the

areas of all its lateral faces.

Model of Square Pyramid Net of Square Pyramid

slant height

vertex

base

lateral face

slant height 

lateral face

side length s of

regular polygon

base

To find the lateral area L of a regular pyramid, refer to the net. The

lateral area is the sum of the areas of the triangles.

L = (^4) ( ^1
2
s) Area of the lateral faces
L = ^1
2
(4s) Commutative Property of Multiplication
L = ^1
2
P The perimeter of the square base P is 4s.
The total surface area of a regular
slant height 
area of the
base #
perimeter of
the base 1
pyramid is the lateral surface area
L plus the area of the base B.
S.A. = B + ^1
2
P
V
s
592_599_C10_L2_895130.indd 594 1/4/10 2:56 PM