Question

the following figure is a rectangle made up of two smaller rectangles.
(a) find the area of the following (in square units).
the dark rectangle (on the left):
the light 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: Calculate the area of the dark rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the dark rectangle, \(l = 9\) and \(w=2\). So, \(A_{dark}=9\times2 = 18\).

Step2: Calculate the area of the light rectangle

For the light rectangle, \(l = 9\) and \(w = x\). So, \(A_{light}=9\times x=9x\).

Step3: Calculate the area as a sum of two areas

\(A_{total}=A_{dark}+A_{light}\). Substitute the values from Step 1 and Step 2: \(A_{total}=18 + 9x\).

Step4: Calculate the area as a product of length and width

The total length of the big - rectangle is \((2 + x)\) and the width is \(9\). Using the formula \(A=l\times w\), we have \(A_{total}=9\times(2 + x)=18+9x\).

Answer:

(a) The dark rectangle: \(18\); The light rectangle: \(9x\)
(b) As a sum of two areas: \(18 + 9x\); As a product of the length and width: \(9(2 + x)=18 + 9x\)