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 rectangle

The area formula for a rectangle is $A = l\times w$. For the dark - rectangle, length is $x$ and width is $6$. So the area $A_1=6x$.

Step2: Find area of light rectangle

For the light - rectangle, length is $5$ and width is $6$. So the area $A_2 = 5\times6=30$.

Step3: Find area as a sum of two areas

The area of the entire figure as a sum of two areas is $A = A_1+A_2=6x + 30$.

Step4: Find area as a product of length and width

The length of the entire rectangle is $x + 5$ and the width is $6$. So the area $A=(x + 5)\times6=6x+30$.

Answer:

The dark rectangle (on the left): $6x$
The light rectangle (on the right): $30$
As a sum of two areas: $6x + 30$
As a product of the length and width: $6(x + 5)$