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: Calculate area of dark rectangle

The formula for the area of a rectangle is $A = l\times w$. For the dark - rectangle on the left, length $l = 7$ and width $w = 3$. So, $A_1=7\times3 = 21$.

Step2: Calculate area of light rectangle

For the light - rectangle on the right, length $l = 7$ and width $w = x$. So, $A_2=7\times x=7x$.

Step3: Find area as sum of two areas

The area of the entire figure as a sum of the two smaller rectangles is $A = A_1 + A_2=21 + 7x$.

Step4: Find area as product of length and width

The length of the entire rectangle is $3 + x$ and the width is $7$. So, $A=7\times(3 + x)=21+7x$.

Answer:

(a) The dark rectangle (on the left): 21
The light rectangle (on the right): $7x$
(b) As a sum of two areas: $21 + 7x$
As a product of the length and width: $7(3 + x)$