Question

the following figure is a rectangle made up of two smaller rectangles. (a) find the area of the following (in square units). the light rectangle (on the left): the dark rectangle (on the right): (b) give the area of the entire figure (in square units) in two different ways. as a sum of two areas: as a product of the length and width:

Explanation:

Step1: Area of a rectangle formula

The area of a rectangle is given by \(A = \text{length}\times\text{width}\).

Step2: Area of the light - colored rectangle

For the light - colored rectangle (left), length \(l = 7\) and width \(w=x\). So, \(A_1=7\times x=7x\).

Step3: Area of the dark - colored rectangle

For the dark - colored rectangle (right), length \(l = 7\) and width \(w = 4\). So, \(A_2=7\times4 = 28\).

Step4: Area as a sum of two areas

The sum of the two areas \(A=A_1 + A_2\). Substituting the values of \(A_1\) and \(A_2\), we get \(A=7x + 28\).

Step5: Area as a product of length and width

The length of the large rectangle is \(7\) and the width is \((x + 4)\). Using the area formula \(A=\text{length}\times\text{width}\), we have \(A=7\times(x + 4)=7x+28\) (using the distributive property \(a(b + c)=ab+ac\) where \(a = 7\), \(b=x\), and \(c = 4\)).

Answer:

(a) The light rectangle: \(7x\); The dark rectangle: \(28\)
(b) As a sum of two areas: \(7x + 28\); As a product of the length and width: \(7(x + 4)=7x+28\)