Exercise 52 Page 21

Practice makes perfect

a We will make a rectangle first, and then identify its dimensions and area.

Rectangle

Let's make the rectangle with algebra tiles!

Dimensions and Area

To identify the dimensions of our rectangle, we have to answer two questions — what is the width

w,

and what is the length

ℓ ?

Looking at the rectangle, we can determine both

ℓ

and

w .

ℓ = 4 and w = x + 2

Since the formula for the area of a rectangle is

A = ℓ w,

we can express the area of our rectangle as below.

A_{Rectangle} = 4 (x + 2)

b To find the areas of both regions we have to identify the dimensions of each of them first.

Green Region

We already know that the length of the full rectangle is

4,

and the green rectangles span throughout the entire length. This means that the length of the green region is also

4 .

Since the width of the whole rectangle was

x + 2,

we can tell that the width of the green region is only

x .

Therefore, we can identify the area.

A_{G} = 4 x

Yellow Region

The length of the yellow region is also

4,

but what is the width? Since there are

2

yellow squares in a row, the width is

2 .

Therefore, we can identify the yellow area.

A_{Y} = 4 \cdot 2 \Rightarrow A_{Y} = 8

c From Part A we know that

4 (x + 2)

is the area of the whole rectangle. In Part B, we found the areas of the green and yellow rectangles. Since the rectangle is made of the green and yellow region, we can make the following conclusion.

A_{Rectangle} = A_{G} + A_{Y}

Let's substitute the expressions for each area.

4 (x + 2) = \underline{4 x + 8}

Now, we completed the statement!

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Rectangle

Dimensions and Area

Green Region

Yellow Region