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: Find area of top rectangle

Use formula $A = lw$. Here, length $l = 4$ and width $w=x$, so $A_1=4x$.

Step2: Find area of bottom rectangle

Use formula $A = lw$. Here, length $l = 4$ and width $w = 7$, so $A_2=4\times7 = 28$.

Step3: Find area of entire figure as sum of two areas

Add areas of two rectangles: $A_{sum}=A_1 + A_2=4x+28$.

Step4: Find area of entire figure as product of length and width

Total length of big - rectangle is $l = 4$ and total width is $w=x + 7$. So $A_{product}=4(x + 7)=4x+28$.

Answer:

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