Question

the following figure is a rectangle made up of two smaller rectangles.
7
2
x
7
(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 dark rectangle

The area formula for a rectangle is $A = l\times w$. For the dark - colored rectangle on the top with length $l = 7$ and width $w = 2$, the area $A_1=7\times2 = 14$.

Step2: Calculate area of light rectangle

For the light - colored rectangle on the bottom with length $l = 7$ and width $w = x$, the area $A_2=7\times x=7x$.

Step3: Calculate area of entire figure as a sum

The area of the entire figure $A_{total}$ as a sum of the two areas is $A_{total}=A_1 + A_2=14 + 7x$.

Step4: Calculate area of entire figure as a product

The length of the entire rectangle is $7$ and the width is $x + 2$. Using the area formula $A=l\times w$, we get $A_{total}=7\times(x + 2)=7x+14$.

Answer:

(a) The dark rectangle (on the top): 14
The light rectangle (on the bottom): 7x
(b) As a sum of two areas: 14 + 7x
As a product of the length and width: 7(x + 2)