Question

(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: Recall area formula for rectangle

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Find area of light - colored rectangle

For the light - colored rectangle on the top with length $x$ and width $4$, the area $A_1=4x$.

Step3: Find area of dark - colored rectangle

For the dark - colored rectangle on the bottom with length $7$ and width $4$, the area $A_2 = 4\times7=28$.

Step4: Find area of entire figure as a sum

The area of the entire figure as a sum of two areas is $A = A_1+A_2=4x + 28$.

Step5: Find area of entire figure as a product

The total length of the combined rectangle is $x + 7$ and the width is $4$. So the area as a product of length and width is $A=4(x + 7)$.

Answer:

(a) The light rectangle (on the top): $4x$
The dark rectangle (on the bottom): $28$
(b) As a sum of two areas: $4x+28$
As a product of the length and width: $4(x + 7)$