Question

so, the area of the entire figure is (x + 5) times 8, which is 8(x + 5). answer for explanation (a) find the area of the following (in square units). the dark rectangle (on the top): 8x the light rectangle (on the bottom): 40 (b) give the area of the entire figure (in square units) in two different ways. as a sum of two areas: 8x + 40 as a product of the length and width: 8(x + 5)

Explanation:

Step1: Analyze dark rectangle area

Area of rectangle = length×width. For dark rectangle with length 8 and width $x$, area is $8\times x = 8x$.

Step2: Analyze light rectangle area

For light rectangle with length 8 and width 5, area is $8\times5=40$.

Step3: Find total area as sum

Total area = area of dark rectangle+area of light rectangle = $8x + 40$.

Step4: Find total area as product

If we consider the combined figure as one rectangle with width 8 and length $(x + 5)$, area is $8(x + 5)$.

Answer:

(a) Dark rectangle area: $8x$; Light rectangle area: $40$
(b) As a sum of two areas: $8x + 40$; As a product of the length and width: $8(x + 5)$