In a school, a auditorium was used for its cultural activities. The shape of the floor of the auditorium is rectangular with dimensions x and y(x > y), has fixed parameter p. 

Based on the above information answer the following questions.

The area (A) of the floor, as a function of x can be expressed as :

$A(x)=\frac{p x-2 x^2}{2}$

Area = x × y = A(x)

as p = 2x + 2y

so $y = \frac{p-2x}{2}$

⇒  A(x) = $\frac{(p-2x)(x)}{2}$

A(x) = $\frac{px-2x^2}{2}$