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 top): the light 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: Calculate area of top rectangle

The formula for the area of a rectangle is $A = l\times w$. For the top - dark rectangle, length $l = 9$ and width $w = 2$. So the area $A_1=9\times2 = 18$.

Step2: Calculate area of bottom rectangle

For the bottom - light rectangle, length $l = 9$ and width $w = x$. So the area $A_2=9\times x=9x$.

Step3: Calculate area of entire figure as sum of two areas

The area of the entire figure $A_{total1}$ as the sum of the areas of the two rectangles is $A_{total1}=A_1 + A_2=18 + 9x$.

Step4: Calculate area of entire figure as product of length and width

The total height of the large rectangle is $h=2 + x$ and the length is $l = 9$. So the area of the entire figure $A_{total2}=9\times(2 + x)=18+9x$.

Answer:

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