area of the whole figure
[tex] = (x + 1)(2x + 3) \\ = x(2x + 3) + 1(2x + 3) \\ = 2 {x}^{2} + 3x + 2x + 3 \\ = {2x}^{2} + 5x + 3[/tex]
area of the unshaded region
[tex] = x(2x) \\ = {2x}^{2} [/tex]
area of the shaded region
[tex] = {2x}^{2} + 5x + 3 - {2x}^{2} \\ = ( {2x}^{2} - {2x}^{2} ) + 5x + 3 \\ = 5x + 3[/tex]
THEREFORE,
THE AREA OF THE FRAME IS C. 5x + 3
