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 top):
the dark rectangle (on the bottom):
(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: Recall rectangle area formula

$A = lw$ (where $l$ is length and $w$ is width)

Step2: Area of light rectangle

$A_{light}=6x$

Step3: Area of dark rectangle

$A_{dark}=6\times7 = 42$

Step4: Total area as sum

$A_{total - sum}=6x + 42$

Step5: Total area as product

Length is $x + 7$, width is 6, so $A_{total - product}=6(x + 7)$

Answer:

(a) The light rectangle: $6x$
The dark rectangle: $42$
(b) As a sum of two areas: $6x + 42$
As a product of the length and width: $6(x + 7)$