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 left): the dark 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: Calculate area of light - left rectangle

The area formula for a rectangle is $A = l\times w$. For the light - left rectangle, length $l = 5$ and width $w = 3$. So $A_1=5\times3 = 15$.

Step2: Calculate area of dark - right rectangle

For the dark - right rectangle, length $l = 5$ and width $w = x$. So $A_2 = 5\times x=5x$.

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

The area of the entire figure $A_{total}$ as a sum of the two areas is $A_{total}=A_1 + A_2=15 + 5x$.

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

The length of the entire rectangle is $5$ and the width is $(3 + x)$. Using the area formula $A=l\times w$, we get $A_{total}=5\times(3 + x)=15+5x$.

Answer:

(a) The light rectangle (on the left): 15
The dark rectangle (on the right): $5x$
(b) As a sum of two areas: $15 + 5x$
As a product of the length and width: $5(3 + x)$