Area and Perimeter with

Algebraic Expressions

Vocabulary needed:•Formula is an equation used to show a

relationship needed in math.•Area is the area inside a two-

dimensional figure.•Perimeter is the distance around a

two-dimensional figure.•Length is also called the base. It is

always perpendicular to the width.•Width is also called the height.

Example #1

The width of a rectangle is 5 more than half of the length. If the length of the rectangle is 42 feet, what is

the area of the rectangle? Drawing a picture will define your variables.

½ L + 5

L= 42W = ½ L + 5W = ½ (42) + 5W = 21 + 5W = 26 feet

A = LWA = 42(26)A = 1,092 feet squared

The area is 1,092 feet squared.

Example #2

The length of a rectangle is twice the width. If the perimeter of the rectangle is 78 inches, what is the

length and the width?

L = 2w

w

P = 2L + 2W78 = 2(2w) + 2w78 = 4w + 2w78 = 6w13 = wSince the length is 2w or 2(13), the length is 26 inches

The width of the rectangle is 13 inches and the length is 26 inches.

Example #3

The perimeter of a rectangle is 96 cm. The length of the rectangle is 8 less than triple the width. Find the

length and the width of the rectangle.

L = 3W – 8

W

P = 2L + 2W 96 = 2(3W – 8) + 2W 96 = 6W – 16 + 2W 96 = 8W – 16112 = 8W 14 = WL = 3(14) – 8 = 34

The width of the rectangle is 14 cm and the length is 34 cm.