The perimeter of a rectangle is given by the formula,
We substitute,
and
into the above formula to obtain the expression,
We now group the x and y terms on the Left Hand Side of the equation to get.
We now divide through by 2 to get,
Therefore the width of the rectangle is
We are asked to determine the area of the given figure. To do that we will divide the figure into a square and a triangle. The area of the square is the product of its dimension, therefore, the area is:
The area of the triangle is given by the following formula:
Where "b" is the base and "h" is its height. Replacing the values:
The total area is the sum of both areas:
replacing the areas:
