The length of the open pit is Area divided by width
A/w = L
L = (12x^2 + 8x)/4x
L = 12x^2 / 4x + 8x/4x
L = 3x + 2
The length of the back part that has to be sealed is 3x + 2 + 2 + 2 = 3x + 8
Area of the White part and the shaded part = L * W
W = 10x -1
L = 3x + 8
Area of the White Part and the Shaded Part = (10x - 1)(3x +8)
The Area of the Shaded Part + White Part = the total area.
Area of the Shaded Part + 12x^2 + 8x = (3x + 8) * (10x - 1)
Expand the right hand side.
Area of the Shaded Part + 12x^2 + 8x = 30x^2 - 3x + 80x - 8 Combine
Area of the Shaded Part + 12x^2 + 8x = 30x^2 + 77x - 8
Answer
Subtract 12x^2 + 8x From both sides.
Area of the Shaded Part = 30x^2 - 12x + 77x - 8x -8
Area of the Shaded Part = 18x^2 + 69x - 8 Answer