The square ABCD of side $$a$$ and the square BEFG of side $$b$$ are drawn next to each other as shown in the figure. Express in terms of $$a$$ and $$b$$ the area of the quadrilateral formed by the mid points of the line segments AB, BE, FC and DG.
[image]

PLACEHOLDER ANSWER - the answer is an expression in $$a$$ and $$b$$. With $$A(0, 0)$$, the midpoints are $$\left(\frac{a}{2}, 0\right)$$, $$\left(a + \frac{b}{2}, 0\right)$$, $$\left(a + \frac{b}{2}, \frac{a + b}{2}\right)$$ and $$\left(\frac{a}{2}, \frac{a + b}{2}\right)$$. These form a square of side $$\frac{a + b}{2}$$, so the area is $$\frac{(a + b)^2}{4}$$.