Answer
The area of the shaded region is $\frac{1}{2}(x^2-y^2)$ square units.
Work Step by Step
RECALL:
(1) The area $A$ of a triangle is given by the formula $A=\frac{1}{2}bh$ where $b$=base and $h$=height.
(2) $(a-b)(a+b)=a^2-b^2$
The given triangle has a base of $x+y$ and a height of $x-y$.
Use the formula in (1) above to obtain:
$A=\frac{1}{2}(x+y)(x-y)$
Use the formula in (2) above to obtain:
$A=\frac{1}{2}(x^2-y^2)$
Thus, the area of the shaded region is $A=\frac{1}{2}(x^2-y^2)$ square units.
