As an afterthought....maybe the patio does not include the pool area and hot tub area?
THEN the area becomes
the previous finding for the entire area MINUS the pool and hot tub areas
pool area = (6x-14)(2x) = 12x^2-28x
hot tub area = x * x = x^2
Subtract these from our previous area ( 32x^2-40x)
32x^2 - 40 x - (12x^2 -28x) - (x^2)
32x^2 - 12x^2 - x^2 - 40x + 28x = 19x^2 - 12x = 'patio' area w/out pool and hot tub areas
Then if x= 9 area =19*81-12*9 = 1431 and cost 1431sqft x $10/sqft =$14310
Area is defined as L x W L as shown in the picture is 8x -10
W = 2x (wall) + 2x (pool) = 4x
so L * W = (8x-10) (4x) = 32x^2 - 40x = Patio Area
Then substitue 9 for x to get the second answer...... (32*81-40*9 = 2232 sq ft
2232 sqft x $10 /sqft = $22320
As an afterthought....maybe the patio does not include the pool area and hot tub area?
THEN the area becomes
the previous finding for the entire area MINUS the pool and hot tub areas
pool area = (6x-14)(2x) = 12x^2-28x
hot tub area = x * x = x^2
Subtract these from our previous area ( 32x^2-40x)
32x^2 - 40 x - (12x^2 -28x) - (x^2)
32x^2 - 12x^2 - x^2 - 40x + 28x = 19x^2 - 12x = 'patio' area w/out pool and hot tub areas
Then if x= 9 area =19*81-12*9 = 1431 and cost 1431sqft x $10/sqft =$14310