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): the light rectangle (on the right): (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: Find area of dark - left rectangle

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

Step2: Find area of light - right rectangle

For the light rectangle on the right with length $5$ and width $9$, using the area formula $A = l\times w$, the area $A_2 = 9\times5=45$.

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

The area of the entire figure $A_{sum}=A_1 + A_2=9x + 45$.

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

The length of the entire rectangle is $x + 5$ and the width is $9$. Using the area formula $A=l\times w$, the area $A_{product}=9(x + 5)$.

Answer:

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