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 area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Find area of light - colored rectangle

For the light - colored rectangle on the top, the length is 6 and the width is $x$. So the area $A_1=6\times x = 6x$.

Step3: Find area of dark - colored rectangle

For the dark - colored rectangle on the bottom, the length is 6 and the width is 7. So the area $A_2 = 6\times7=42$.

Step4: Find area of entire figure as a sum

The area of the entire figure as a sum of the two areas is $A = A_1+A_2=6x + 42$.

Step5: Find area of entire figure as a product

The length of the entire rectangle is $x + 7$ and the width is 6. So the area $A=6\times(x + 7)=6x+42$.

Answer:

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