Answer
$\text{Area}=\frac{1}{2}x^{2}+\frac{11}{2}x+15$
Work Step by Step
$\text{Area of the shaded region}
$$=\text{Area of the unshaded isosceles triangle}$
$=\frac{1}{2}\times\text{base}\times\text{height}$
$=\frac{1}{2}(x+6)(x+5)$
Using FOIL (First Outer Inner Last) method, we obtain
$\text{Area}=\frac{1}{2}(x^{2}+5x+6x+30)$
Combining like terms, we have
$\text{Area}=\frac{1}{2}(x^{2}+11x+30)$
Using distributive property, we get
$\text{Area}=\frac{1}{2}x^{2}+\frac{11}{2}x+15$
