Answer
$\text{Area}=p^{2}-2p-3$
Work Step by Step
$\text{Area of the shaded region}=\text{Area of the triangle}=\frac{1}{2}\times\text{base}\times\text{height}$
$\implies \text{Area}=\frac{1}{2}(p+1)(2p-6)$
Using FOIL (First Outer Inner Last) method, we have
$\text{Area}=\frac{1}{2}[2p^{2}+(-6p)+2p+(-6)]$
Combining like terms, we get
$\text{Area}=\frac{1}{2}(2p^{2}-4p-6)$
Using distributive property, we obtain
$\text{Area}=p^{2}-2p-3$
