Question

The Smith family is designing new plans for an in-ground pool. Mr. Smith draws a rectangular shape with a length that is 5 feet longer than the height.
Mr. Smith wants to add a 2 foot concrete walkway around the edge of the pool. Write a polynomial expression, in simplified form, that represents the total area of the pool and the walkway. Show and explain how you got the area of the pool and the walkway.

Answer 1

Answer:
total area = w^2 + 13w + 36 ft^2

Explanation:
The final pool and the sideways will be as shown in the attachment

1- We will get the area of the pool:
length of pool = w + 5
width of pool = w
area of pool = length * width
area of pool = w (w+5) square ft ...........> I

2- We will get the area of the sideways:
The side way is composed of the two blue rectangles and the two green ones
Therefore:
area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)
a- getting the area of the blue rectangle:
length = w + 5 + 2 + 2 = w+9
width = 2
area of blue rectangle = length * width
area of blue rectangle = 2(w+9) square ft ..........> a
b- getting the area of the green rectangle:
length = w
width = 2
area of green rectangle = length * width
area of green rectangle = 2w square ft ..............> b
c- getting area of sideways:
as mentioned before:
area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)
area of sideways = 2*equation a + 2*equation b
area of sideways = 2 (2(w+9)) + 2(2w)
area of sideways = 4(w+9) + 4w
area of sideways = 4w + 36 + 4w
area of sideways = 8w + 36 ...........> II

3- getting the total area:
total area = area of pool + area of sideways
total area = equation I + equation II
total area = w (w+5) + 8w + 36
total area = w^2 + 5w + 8w + 36
total area = w^2 + 13w + 36 ft^2

Hope this helps :)