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: Calculate area of light - top rectangle

The area formula for a rectangle is $A = l\times w$. For the light - top rectangle, $l = 5$ and $w = 3$. So $A_{1}=3\times5 = 15$.

Step2: Calculate area of dark - bottom rectangle

For the dark - bottom rectangle, $l = x$ and $w = 3$. So $A_{2}=3\times x=3x$.

Step3: Find area as sum of two areas

The area of the entire figure as a sum of two areas is $A = A_{1}+A_{2}=15 + 3x$.

Step4: Find area as product of length and width

The length of the entire rectangle is $5 + x$ and the width is 3. So $A=3\times(5 + x)=15+3x$.

Answer:

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