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): 9
the light rectangle (on the right): 9
(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 area of dark rectangle

The area formula for a rectangle is $A = l\times w$. For the dark - rectangle with length $x$ and width $9$, the area $A_1=9x$.

Step2: Calculate area of light rectangle

For the light - rectangle with length $5$ and width $9$, the area $A_2 = 9\times5=45$.

Step3: Find area as sum of two areas

The area of the entire figure as a sum of two areas is $A = A_1+A_2=9x + 45$.

Step4: Find area as product of length and width

The length of the entire rectangle is $x + 5$ and the width is $9$. So the area as a product of length and width is $A=9(x + 5)$.

Answer:

(a) The dark rectangle: $9x$; The light rectangle: $45$
(b) As a sum of two areas: $9x + 45$
As a product of the length and width: $9(x + 5)$