To find the area of the shaded part we have to subtract the rectangle area from the triangle area :
[tex]s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1) \\ [/tex]
[tex]s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x) \\ [/tex]
[tex]s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x \\ [/tex]
[tex]s = 24 {x}^{2} + 6x - 3 {x}^{2} - x[/tex]
[tex]s = 24 {x}^{2} - 3 {x}^{2} + 6x - x[/tex]
[tex]s = 21 {x}^{2} + 5x[/tex]
And we're done
Have a great day ♡
