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 top rectangle

The area formula for a rectangle is $A = l\times w$. For the light - colored (top) rectangle, $l = 5$ and $w = 3$. So, $A_{top}=5\times3 = 15$.

Step2: Calculate area of bottom rectangle

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

Step3: Find area as sum of two areas

The area of the entire figure as a sum of the two smaller rectangles is $A = A_{top}+A_{bottom}=15 + 3x$.

Step4: Find area as product of length and width

The length of the entire rectangle is $5 + x$ and the width is 3. Using the area formula $A=l\times w$, we get $A=(5 + x)\times3=15+3x$.

Answer:

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