22. Three squares, with side-lengths 2, are placed together edge-toedge to make an L-shape. The L-shape is placed inside a rectangle so that all five vertices of the $\mathrm{L}$-shape lie on the rectangle, one of them at the midpoint of an edge, as shown.
What is the area of the rectangle?
A 16
B 18
C 20
D 22
E 24
22. E Let the area of each of the three squares be $S$. Then the areas of triangles $A J I, A J B, B K C, C K D$ and $G L F$ are all equal to $\frac{1}{2} S$. Also, the areas of triangles $D E F$ and $G H I$ are both equal to $\frac{1}{4} S$. So the total area inside the rectangle, but outside the three squares, is $5 \times \frac{1}{2} S+2 \times \frac{1}{4} S=3 S$. Therefore the area of the rectangle is $6 S=6 \times 2 \times 2=24$.
(It is left as an exercise for the reader to show that the height and width of the rectangle are $4 \sqrt{2}$ and $3 \sqrt{2}$ respectively and therefore that its area is $4 \sqrt{2} \times 3 \sqrt{2}=24$.)