27. As shown in the figure,
$$
A B \perp B C, B C \perp C D \text {, }
$$
$B C$ is tangent to the circle $O$ with $A D$ as the diameter. In which of the following cases is the area of $A B C D$ an integer?
(A) $A B=3, C D=1$.
(B) $A B=5, C D=2$.
(C) $A B=7, C D=3$.
(D) $A B=8, C D=4$.
(E) $A B=11, C D=5$.
27
D
27. $ABCD$ is a trapezoid, then its area is $\frac{BC(AB+CD)}{2}$. In the figure, $BCDN$ is a rectangle, $BN = CD, \angle OEB=90^{\circ}$,
$\therefore OE \parallel CD, M$ is the midpoint of $BC$.
Also, $\because BE^2 = BN \cdot BA$,
$\therefore BC = 2 \sqrt{CD \cdot BA}$.
And $S = (AB + CD) \sqrt{AB \cdot CD}$.
When $AB \cdot CD$ is a perfect square, $S$ is an integer, hence the answer is (D).