1978 AHSME Problem 25

Let a be a positive number. Consider the set S of all points whose rectangular coordinates (x, y ) satisfy all of the following conditions:

\begin{array}{l} \text{(i) }\frac{a}{2}\le x\le 2a\qquad \text{(ii) }\frac{a}{2}\le y\le 2a\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x \end{array}

The boundary of set S is a polygon with

\textbf{(A) }3\text{ sides}\qquad \textbf{(B) }4\text{ sides}\qquad \textbf{(C) }5\text{ sides}\qquad \textbf{(D) }6\text{ sides}\qquad \textbf{(E) }7\text{ sides}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.